Solve 2[5(x+1)-2(1+x)^2-2x(5-x)+1]=26

$$2 [ 5 ( x + 1 ) - 2 ( 1 + x ) ^ { 2 } - 2 x ( 5 - x ) + 1 ] = 26$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Divide both sides by 2.

$$5\left(x+1\right)-2\left(1+x\right)^{2}-2x\left(5-x\right)+1=\frac{26}{2}$$

Divide 26 by 2 to get 13.

$$5\left(x+1\right)-2\left(1+x\right)^{2}-2x\left(5-x\right)+1=13$$

Use the distributive property to multiply 5 by x+1.

$$5x+5-2\left(1+x\right)^{2}-2x\left(5-x\right)+1=13$$

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

$$5x+5-2\left(1+2x+x^{2}\right)-2x\left(5-x\right)+1=13$$

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

$$5x+5-2-4x-2x^{2}-2x\left(5-x\right)+1=13$$

Subtract 2 from 5 to get 3.

$$5x+3-4x-2x^{2}-2x\left(5-x\right)+1=13$$

Combine 5x and -4x to get x.

$$x+3-2x^{2}-2x\left(5-x\right)+1=13$$

Subtract 1 from both sides.

$$x+3-2x^{2}-2x\left(5-x\right)=13-1$$

Subtract 1 from 13 to get 12.

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

Use the distributive property to multiply -2x by 5-x.

$$x+3-2x^{2}-10x+2x^{2}=12$$

Combine x and -10x to get -9x.

$$-9x+3-2x^{2}+2x^{2}=12$$

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

$$-9x+3=12$$

Subtract 3 from both sides.

$$-9x=12-3$$

Subtract 3 from 12 to get 9.

$$-9x=9$$

Divide both sides by -9.

$$x=\frac{9}{-9}$$

Divide 9 by -9 to get -1.

$$x=-1$$