Solve (7-x)(7+x)+3x^2=x(x+7)+x^2

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

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Consider \left(7-x\right)\left(7+x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 7.

$$49-x^{2}+3x^{2}=x\left(x+7\right)+x^{2}$$

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

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

Use the distributive property to multiply x by x+7.

$$49+2x^{2}=x^{2}+7x+x^{2}$$

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

$$49+2x^{2}=2x^{2}+7x$$

Subtract 2x^{2} from both sides.

$$49+2x^{2}-2x^{2}=7x$$

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

$$49=7x$$

Swap sides so that all variable terms are on the left hand side.

$$7x=49$$

Divide both sides by 7.

$$x=\frac{49}{7}$$

Divide 49 by 7 to get 7.

$$x=7$$