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

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

Step 1

Simplify $x (2 x - 3)$ .

Rewrite.

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

Simplify by multiplying through.

Apply the distributive property.

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

Reorder.

Rewrite using the commutative property of multiplication.

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

Move $- 3$ to the left of $x$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Step 2

Simplify $(2 x + 1) (x - 4)$ .

Expand $(2 x + 1) (x - 4)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 4$ by $2$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 4$ by $1$ .

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

Add $- 8 x$ and $x$ .

$2 x^{2} - 3 x = 2 x^{2} - 7 x - 4$

Step 3

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

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

$2 x^{2} - 3 x - 2 x^{2} = - 7 x - 4$

Add $7 x$ to both sides of the equation.

$2 x^{2} - 3 x - 2 x^{2} + 7 x = - 4$

Combine the opposite terms in $2 x^{2} - 3 x - 2 x^{2} + 7 x$ .

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

$- 3 x + 0 + 7 x = - 4$

Add $- 3 x$ and $0$ .

$- 3 x + 7 x = - 4$

Add $- 3 x$ and $7 x$ .

$4 x = - 4$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $4$ .

$x = - 1$

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

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