Solve (6x-1)^2+70x-11(x+2)^2=(5x+2)^2-7x

$$( 6 x - 1 ) ^ { 2 } + 70 x - 11 ( x + 2 ) ^ { 2 } = ( 5 x + 2 ) ^ { 2 } - 7 x$$

Solve for x

$$x=47$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x-1\right)^{2}.

$$36x^{2}-12x+1+70x-11\left(x+2\right)^{2}=\left(5x+2\right)^{2}-7x$$

Combine -12x and 70x to get 58x.

$$36x^{2}+58x+1-11\left(x+2\right)^{2}=\left(5x+2\right)^{2}-7x$$

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

$$36x^{2}+58x+1-11\left(x^{2}+4x+4\right)=\left(5x+2\right)^{2}-7x$$

Use the distributive property to multiply -11 by x^{2}+4x+4.

$$36x^{2}+58x+1-11x^{2}-44x-44=\left(5x+2\right)^{2}-7x$$

Combine 36x^{2} and -11x^{2} to get 25x^{2}.

$$25x^{2}+58x+1-44x-44=\left(5x+2\right)^{2}-7x$$

Combine 58x and -44x to get 14x.

$$25x^{2}+14x+1-44=\left(5x+2\right)^{2}-7x$$

Subtract 44 from 1 to get -43.

$$25x^{2}+14x-43=\left(5x+2\right)^{2}-7x$$

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

$$25x^{2}+14x-43=25x^{2}+20x+4-7x$$

Combine 20x and -7x to get 13x.

$$25x^{2}+14x-43=25x^{2}+13x+4$$

Subtract 25x^{2} from both sides.

$$25x^{2}+14x-43-25x^{2}=13x+4$$

Combine 25x^{2} and -25x^{2} to get 0.

$$14x-43=13x+4$$

Subtract 13x from both sides.

$$14x-43-13x=4$$

Combine 14x and -13x to get x.

$$x-43=4$$

Add 43 to both sides.

$$x=4+43$$

Add 4 and 43 to get 47.

$$x=47$$