Solve left(5x-10right)^2-left(-x+10right)^2=-6left(2x-1right)left(7-2xright)-10

$${ \left(5x-10 \right) }^{ 2 } - { \left(-x+10 \right) }^{ 2 } = -6 \left( 2x-1 \right) \left( 7-2x \right) -10$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5x-10\right)^{2}.

$$25x^{2}-100x+100-\left(-x+10\right)^{2}=-6\left(2x-1\right)\left(7-2x\right)-10$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-x+10\right)^{2}.

$$25x^{2}-100x+100-\left(\left(-x\right)^{2}+20\left(-x\right)+100\right)=-6\left(2x-1\right)\left(7-2x\right)-10$$

Calculate -x to the power of 2 and get x^{2}.

$$25x^{2}-100x+100-\left(x^{2}+20\left(-x\right)+100\right)=-6\left(2x-1\right)\left(7-2x\right)-10$$

To find the opposite of x^{2}+20\left(-x\right)+100, find the opposite of each term.

$$25x^{2}-100x+100-x^{2}-20\left(-x\right)-100=-6\left(2x-1\right)\left(7-2x\right)-10$$

Combine 25x^{2} and -x^{2} to get 24x^{2}.

$$24x^{2}-100x+100-20\left(-x\right)-100=-6\left(2x-1\right)\left(7-2x\right)-10$$

Multiply -20 and -1 to get 20.

$$24x^{2}-100x+100+20x-100=-6\left(2x-1\right)\left(7-2x\right)-10$$

Combine -100x and 20x to get -80x.

$$24x^{2}-80x+100-100=-6\left(2x-1\right)\left(7-2x\right)-10$$

Subtract 100 from 100 to get 0.

$$24x^{2}-80x=-6\left(2x-1\right)\left(7-2x\right)-10$$

Use the distributive property to multiply -6 by 2x-1.

$$24x^{2}-80x=\left(-12x+6\right)\left(7-2x\right)-10$$

Use the distributive property to multiply -12x+6 by 7-2x and combine like terms.

$$24x^{2}-80x=-96x+24x^{2}+42-10$$

Subtract 10 from 42 to get 32.

$$24x^{2}-80x=-96x+24x^{2}+32$$

Add 96x to both sides.

$$24x^{2}-80x+96x=24x^{2}+32$$

Combine -80x and 96x to get 16x.

$$24x^{2}+16x=24x^{2}+32$$

Subtract 24x^{2} from both sides.

$$24x^{2}+16x-24x^{2}=32$$

Combine 24x^{2} and -24x^{2} to get 0.

$$16x=32$$

Divide both sides by 16.

$$x=\frac{32}{16}$$

Divide 32 by 16 to get 2.

$$x=2$$