Solve for x 4x(x-2)=(2x+1)(2x-3)

$4 x (x - 2) = (2 x + 1) (2 x - 3)$

Simplify $4 x (x - 2)$ .

Start simplifying.

$0 + 0 + 4 x (x - 2) = (2 x + 1) (2 x - 3)$

Simplify by adding zeros.

$4 x (x - 2) = (2 x + 1) (2 x - 3)$

Apply the distributive property.

$4 x \cdot x + 4 x \cdot - 2 = (2 x + 1) (2 x - 3)$

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

Move $x$ .

$4 (x \cdot x) + 4 x \cdot - 2 = (2 x + 1) (2 x - 3)$

Multiply $x$ by $x$ .

$4 x^{2} + 4 x \cdot - 2 = (2 x + 1) (2 x - 3)$

Multiply $- 2$ by $4$ .

$4 x^{2} - 8 x = (2 x + 1) (2 x - 3)$

Simplify $(2 x + 1) (2 x - 3)$ .

Expand $(2 x + 1) (2 x - 3)$ using the FOIL Method.

Apply the distributive property.

$4 x^{2} - 8 x = 2 x (2 x - 3) + 1 (2 x - 3)$

Apply the distributive property.

$4 x^{2} - 8 x = 2 x (2 x) + 2 x \cdot - 3 + 1 (2 x - 3)$

Apply the distributive property.

$4 x^{2} - 8 x = 2 x (2 x) + 2 x \cdot - 3 + 1 (2 x) + 1 \cdot - 3$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 x^{2} - 8 x = 2 \cdot 2 x \cdot x + 2 x \cdot - 3 + 1 (2 x) + 1 \cdot - 3$

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

Move $x$ .

$4 x^{2} - 8 x = 2 \cdot 2 (x \cdot x) + 2 x \cdot - 3 + 1 (2 x) + 1 \cdot - 3$

Multiply $x$ by $x$ .

$4 x^{2} - 8 x = 2 \cdot 2 x^{2} + 2 x \cdot - 3 + 1 (2 x) + 1 \cdot - 3$

Multiply $2$ by $2$ .

$4 x^{2} - 8 x = 4 x^{2} + 2 x \cdot - 3 + 1 (2 x) + 1 \cdot - 3$

Multiply $- 3$ by $2$ .

$4 x^{2} - 8 x = 4 x^{2} - 6 x + 1 (2 x) + 1 \cdot - 3$

Multiply $2 x$ by $1$ .

$4 x^{2} - 8 x = 4 x^{2} - 6 x + 2 x + 1 \cdot - 3$

Multiply $- 3$ by $1$ .

$4 x^{2} - 8 x = 4 x^{2} - 6 x + 2 x - 3$

Add $- 6 x$ and $2 x$ .

$4 x^{2} - 8 x = 4 x^{2} - 4 x - 3$

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

Subtract $4 x^{2}$ from both sides of the equation.

$4 x^{2} - 8 x - 4 x^{2} = - 4 x - 3$

Add $4 x$ to both sides of the equation.

$4 x^{2} - 8 x - 4 x^{2} + 4 x = - 3$

Combine the opposite terms in $4 x^{2} - 8 x - 4 x^{2} + 4 x$ .

Subtract $4 x^{2}$ from $4 x^{2}$ .

$- 8 x + 0 + 4 x = - 3$

Add $- 8 x$ and $0$ .

$- 8 x + 4 x = - 3$

Add $- 8 x$ and $4 x$ .

$- 4 x = - 3$

Divide each term in $- 4 x = - 3$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 3$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 3}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 3}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 3}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{3}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}$

Decimal Form:

$x = 0.75$

Solve for x 4x(x-2)=(2x+1)(2x-3)

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