Solve 7(x-4)^2-3(x+5)^2=4(x+1)(x-1)-2

$$7 ( x - 4 ) ^ { 2 } - 3 ( x + 5 ) ^ { 2 } = 4 ( x + 1 ) ( x - 1 ) - 2$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$7\left(x^{2}-8x+16\right)-3\left(x+5\right)^{2}=4\left(x+1\right)\left(x-1\right)-2$$

Use the distributive property to multiply 7 by x^{2}-8x+16.

$$7x^{2}-56x+112-3\left(x+5\right)^{2}=4\left(x+1\right)\left(x-1\right)-2$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$7x^{2}-56x+112-3\left(x^{2}+10x+25\right)=4\left(x+1\right)\left(x-1\right)-2$$

Use the distributive property to multiply -3 by x^{2}+10x+25.

$$7x^{2}-56x+112-3x^{2}-30x-75=4\left(x+1\right)\left(x-1\right)-2$$

Combine 7x^{2} and -3x^{2} to get 4x^{2}.

$$4x^{2}-56x+112-30x-75=4\left(x+1\right)\left(x-1\right)-2$$

Combine -56x and -30x to get -86x.

$$4x^{2}-86x+112-75=4\left(x+1\right)\left(x-1\right)-2$$

Subtract 75 from 112 to get 37.

$$4x^{2}-86x+37=4\left(x+1\right)\left(x-1\right)-2$$

Use the distributive property to multiply 4 by x+1.

$$4x^{2}-86x+37=\left(4x+4\right)\left(x-1\right)-2$$

Use the distributive property to multiply 4x+4 by x-1 and combine like terms.

$$4x^{2}-86x+37=4x^{2}-4-2$$

Subtract 2 from -4 to get -6.

$$4x^{2}-86x+37=4x^{2}-6$$

Subtract 4x^{2} from both sides.

$$4x^{2}-86x+37-4x^{2}=-6$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-86x+37=-6$$

Subtract 37 from both sides.

$$-86x=-6-37$$

Subtract 37 from -6 to get -43.

$$-86x=-43$$

Divide both sides by -86.

$$x=\frac{-43}{-86}$$

Reduce the fraction \frac{-43}{-86} to lowest terms by extracting and canceling out -43.

$$x=\frac{1}{2}$$