Solve 2x(x-4)-(2x+3)(x-4)=4x(2x-3)-8(1-x)^2

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

Solve for x

$$x = \frac{20}{7} = 2\frac{6}{7} \approx 2.857142857$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x by x-4.

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

Use the distributive property to multiply 2x+3 by x-4 and combine like terms.

$$2x^{2}-8x-\left(2x^{2}-5x-12\right)=4x\left(2x-3\right)-8\left(1-x\right)^{2}$$

To find the opposite of 2x^{2}-5x-12, find the opposite of each term.

$$2x^{2}-8x-2x^{2}+5x+12=4x\left(2x-3\right)-8\left(1-x\right)^{2}$$

Combine 2x^{2} and -2x^{2} to get 0.

$$-8x+5x+12=4x\left(2x-3\right)-8\left(1-x\right)^{2}$$

Combine -8x and 5x to get -3x.

$$-3x+12=4x\left(2x-3\right)-8\left(1-x\right)^{2}$$

Use the distributive property to multiply 4x by 2x-3.

$$-3x+12=8x^{2}-12x-8\left(1-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x\right)^{2}.

$$-3x+12=8x^{2}-12x-8\left(1-2x+x^{2}\right)$$

Use the distributive property to multiply -8 by 1-2x+x^{2}.

$$-3x+12=8x^{2}-12x-8+16x-8x^{2}$$

Combine -12x and 16x to get 4x.

$$-3x+12=8x^{2}+4x-8-8x^{2}$$

Combine 8x^{2} and -8x^{2} to get 0.

$$-3x+12=4x-8$$

Subtract 4x from both sides.

$$-3x+12-4x=-8$$

Combine -3x and -4x to get -7x.

$$-7x+12=-8$$

Subtract 12 from both sides.

$$-7x=-8-12$$

Subtract 12 from -8 to get -20.

$$-7x=-20$$

Divide both sides by -7.

$$x=\frac{-20}{-7}$$

Fraction \frac{-20}{-7} can be simplified to \frac{20}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{20}{7}$$