Solve 4+2left(7-xright)^2+7-x+2x(7-x)-49=0

$$4+2 { \left(7-x \right) }^{ 2 } +7-x+2x(7-x)-49=0$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7-x\right)^{2}.

$$4+2\left(49-14x+x^{2}\right)+7-x+2x\left(7-x\right)-49=0$$

Use the distributive property to multiply 2 by 49-14x+x^{2}.

$$4+98-28x+2x^{2}+7-x+2x\left(7-x\right)-49=0$$

Add 4 and 98 to get 102.

$$102-28x+2x^{2}+7-x+2x\left(7-x\right)-49=0$$

Add 102 and 7 to get 109.

$$109-28x+2x^{2}-x+2x\left(7-x\right)-49=0$$

Combine -28x and -x to get -29x.

$$109-29x+2x^{2}+2x\left(7-x\right)-49=0$$

Use the distributive property to multiply 2x by 7-x.

$$109-29x+2x^{2}+14x-2x^{2}-49=0$$

Combine -29x and 14x to get -15x.

$$109-15x+2x^{2}-2x^{2}-49=0$$

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

$$109-15x-49=0$$

Subtract 49 from 109 to get 60.

$$60-15x=0$$

Subtract 60 from both sides. Anything subtracted from zero gives its negation.

$$-15x=-60$$

Divide both sides by -15.

$$x=\frac{-60}{-15}$$

Divide -60 by -15 to get 4.

$$x=4$$