Solve for x (4x-1)(5x+4)-20x^2=18

$(4 x - 1) (5 x + 4) - 20 x^{2} = 18$

Simplify $(4 x - 1) (5 x + 4) - 20 x^{2}$ .

Simplify each term.

Expand $(4 x - 1) (5 x + 4)$ using the FOIL Method.

Apply the distributive property.

$4 x (5 x + 4) - 1 (5 x + 4) - 20 x^{2} = 18$

Apply the distributive property.

$4 x (5 x) + 4 x \cdot 4 - 1 (5 x + 4) - 20 x^{2} = 18$

Apply the distributive property.

$4 x (5 x) + 4 x \cdot 4 - 1 (5 x) - 1 \cdot 4 - 20 x^{2} = 18$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 5 x \cdot x + 4 x \cdot 4 - 1 (5 x) - 1 \cdot 4 - 20 x^{2} = 18$

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

Move $x$ .

$4 \cdot 5 (x \cdot x) + 4 x \cdot 4 - 1 (5 x) - 1 \cdot 4 - 20 x^{2} = 18$

Multiply $x$ by $x$ .

$4 \cdot 5 x^{2} + 4 x \cdot 4 - 1 (5 x) - 1 \cdot 4 - 20 x^{2} = 18$

Multiply $4$ by $5$ .

$20 x^{2} + 4 x \cdot 4 - 1 (5 x) - 1 \cdot 4 - 20 x^{2} = 18$

Multiply $4$ by $4$ .

$20 x^{2} + 16 x - 1 (5 x) - 1 \cdot 4 - 20 x^{2} = 18$

Multiply $5$ by $- 1$ .

$20 x^{2} + 16 x - 5 x - 1 \cdot 4 - 20 x^{2} = 18$

Multiply $- 1$ by $4$ .

$20 x^{2} + 16 x - 5 x - 4 - 20 x^{2} = 18$

Subtract $5 x$ from $16 x$ .

$20 x^{2} + 11 x - 4 - 20 x^{2} = 18$

Combine the opposite terms in $20 x^{2} + 11 x - 4 - 20 x^{2}$ .

Subtract $20 x^{2}$ from $20 x^{2}$ .

$11 x - 4 + 0 = 18$

Add $11 x - 4$ and $0$ .

$11 x - 4 = 18$

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

Add $4$ to both sides of the equation.

$11 x = 18 + 4$

Add $18$ and $4$ .

$11 x = 22$

Divide each term in $11 x = 22$ by $11$ and simplify.

Divide each term in $11 x = 22$ by $11$ .

$\frac{11 x}{11} = \frac{22}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{22}{11}$

Divide $x$ by $1$ .

$x = \frac{22}{11}$

Simplify the right side.

Divide $22$ by $11$ .

$x = 2$

Solve for x (4x-1)(5x+4)-20x^2=18

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