Solve for x (4-5x)(4x-5)=(10x-3)(7-2x)

$(4 - 5 x) (4 x - 5) = (10 x - 3) (7 - 2 x)$

Simplify $(4 - 5 x) (4 x - 5)$ .

Start simplifying.

$0 + 0 + (4 - 5 x) (4 x - 5) = (10 x - 3) (7 - 2 x)$

Simplify by adding zeros.

$(4 - 5 x) (4 x - 5) = (10 x - 3) (7 - 2 x)$

Expand $(4 - 5 x) (4 x - 5)$ using the FOIL Method.

Apply the distributive property.

$4 (4 x - 5) - 5 x (4 x - 5) = (10 x - 3) (7 - 2 x)$

Apply the distributive property.

$4 (4 x) + 4 \cdot - 5 - 5 x (4 x - 5) = (10 x - 3) (7 - 2 x)$

Apply the distributive property.

$4 (4 x) + 4 \cdot - 5 - 5 x (4 x) - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 x + 4 \cdot - 5 - 5 x (4 x) - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Multiply $4$ by $- 5$ .

$16 x - 20 - 5 x (4 x) - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Rewrite using the commutative property of multiplication.

$16 x - 20 - 5 \cdot 4 x \cdot x - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$16 x - 20 - 5 \cdot 4 (x \cdot x) - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Multiply $x$ by $x$ .

$16 x - 20 - 5 \cdot 4 x^{2} - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Multiply $- 5$ by $4$ .

$16 x - 20 - 20 x^{2} - 5 x \cdot - 5 = (10 x - 3) (7 - 2 x)$

Multiply $- 5$ by $- 5$ .

$16 x - 20 - 20 x^{2} + 25 x = (10 x - 3) (7 - 2 x)$

Add $16 x$ and $25 x$ .

$41 x - 20 - 20 x^{2} = (10 x - 3) (7 - 2 x)$

Simplify $(10 x - 3) (7 - 2 x)$ .

Expand $(10 x - 3) (7 - 2 x)$ using the FOIL Method.

Apply the distributive property.

$41 x - 20 - 20 x^{2} = 10 x (7 - 2 x) - 3 (7 - 2 x)$

Apply the distributive property.

$41 x - 20 - 20 x^{2} = 10 x \cdot 7 + 10 x (- 2 x) - 3 (7 - 2 x)$

Apply the distributive property.

$41 x - 20 - 20 x^{2} = 10 x \cdot 7 + 10 x (- 2 x) - 3 \cdot 7 - 3 (- 2 x)$

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $10$ .

$41 x - 20 - 20 x^{2} = 70 x + 10 x (- 2 x) - 3 \cdot 7 - 3 (- 2 x)$

Rewrite using the commutative property of multiplication.

$41 x - 20 - 20 x^{2} = 70 x + 10 \cdot - 2 x \cdot x - 3 \cdot 7 - 3 (- 2 x)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$41 x - 20 - 20 x^{2} = 70 x + 10 \cdot - 2 (x \cdot x) - 3 \cdot 7 - 3 (- 2 x)$

Multiply $x$ by $x$ .

$41 x - 20 - 20 x^{2} = 70 x + 10 \cdot - 2 x^{2} - 3 \cdot 7 - 3 (- 2 x)$

Multiply $10$ by $- 2$ .

$41 x - 20 - 20 x^{2} = 70 x - 20 x^{2} - 3 \cdot 7 - 3 (- 2 x)$

Multiply $- 3$ by $7$ .

$41 x - 20 - 20 x^{2} = 70 x - 20 x^{2} - 21 - 3 (- 2 x)$

Multiply $- 2$ by $- 3$ .

$41 x - 20 - 20 x^{2} = 70 x - 20 x^{2} - 21 + 6 x$

Add $70 x$ and $6 x$ .

$41 x - 20 - 20 x^{2} = 76 x - 20 x^{2} - 21$

Move all terms containing $x$ to the left side of the equation.

Subtract $76 x$ from both sides of the equation.

$41 x - 20 - 20 x^{2} - 76 x = - 20 x^{2} - 21$

Add $20 x^{2}$ to both sides of the equation.

$41 x - 20 - 20 x^{2} - 76 x + 20 x^{2} = - 21$

Combine the opposite terms in $41 x - 20 - 20 x^{2} - 76 x + 20 x^{2}$ .

Add $- 20 x^{2}$ and $20 x^{2}$ .

$41 x - 20 - 76 x + 0 = - 21$

Add $41 x - 20 - 76 x$ and $0$ .

$41 x - 20 - 76 x = - 21$

Subtract $76 x$ from $41 x$ .

$- 35 x - 20 = - 21$

Move all terms not containing $x$ to the right side of the equation.

Add $20$ to both sides of the equation.

$- 35 x = - 21 + 20$

Add $- 21$ and $20$ .

$- 35 x = - 1$

Divide each term in $- 35 x = - 1$ by $- 35$ and simplify.

Divide each term in $- 35 x = - 1$ by $- 35$ .

$\frac{- 35 x}{- 35} = \frac{- 1}{- 35}$

Simplify the left side.

Cancel the common factor of $- 35$ .

Cancel the common factor.

$\frac{- 35 x}{- 35} = \frac{- 1}{- 35}$

Divide $x$ by $1$ .

$x = \frac{- 1}{- 35}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{1}{35}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{35}$

Decimal Form:

$x = 0.0\overline{285714}$

Solve for x (4-5x)(4x-5)=(10x-3)(7-2x)

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