Solve (3x-7)^2-5(2x-4)(x-2)=-(x+2)^2+4x+9

$$( 3 x - 7 ) ^ { 2 } - 5 ( 2 x - 4 ) ( x - 2 ) = - ( x + 2 ) ^ { 2 } + 4 x + 9$$

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(3x-7\right)^{2}.

$$9x^{2}-42x+49-5\left(2x-4\right)\left(x-2\right)=-\left(x+2\right)^{2}+4x+9$$

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

$$9x^{2}-42x+49-5\left(2x-4\right)\left(x-2\right)=-\left(x^{2}+4x+4\right)+4x+9$$

To find the opposite of x^{2}+4x+4, find the opposite of each term.

$$9x^{2}-42x+49-5\left(2x-4\right)\left(x-2\right)=-x^{2}-4x-4+4x+9$$

Combine -4x and 4x to get 0.

$$9x^{2}-42x+49-5\left(2x-4\right)\left(x-2\right)=-x^{2}-4+9$$

Add -4 and 9 to get 5.

$$9x^{2}-42x+49-5\left(2x-4\right)\left(x-2\right)=-x^{2}+5$$

Add x^{2} to both sides.

$$9x^{2}-42x+49-5\left(2x-4\right)\left(x-2\right)+x^{2}=5$$

Use the distributive property to multiply -5 by 2x-4.

$$9x^{2}-42x+49+\left(-10x+20\right)\left(x-2\right)+x^{2}=5$$

Use the distributive property to multiply -10x+20 by x-2 and combine like terms.

$$9x^{2}-42x+49-10x^{2}+40x-40+x^{2}=5$$

Combine 9x^{2} and -10x^{2} to get -x^{2}.

$$-x^{2}-42x+49+40x-40+x^{2}=5$$

Combine -42x and 40x to get -2x.

$$-x^{2}-2x+49-40+x^{2}=5$$

Subtract 40 from 49 to get 9.

$$-x^{2}-2x+9+x^{2}=5$$

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

$$-2x+9=5$$

Subtract 9 from both sides.

$$-2x=5-9$$

Subtract 9 from 5 to get -4.

$$-2x=-4$$

Divide both sides by -2.

$$x=\frac{-4}{-2}$$

Divide -4 by -2 to get 2.

$$x=2$$