Solve left(3x-7right)^2-5(2x+1)(x-2)=-x^2-(3x-1)

$${ \left(3x-7 \right) }^{ 2 } -5(2x+1)(x-2)=- { x }^{ 2 } -(3x-1)$$

Solve for x

$$x = \frac{29}{12} = 2\frac{5}{12} \approx 2.416666667$$

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}.

$$9x^{2}-42x+49-5\left(2x+1\right)\left(x-2\right)=-x^{2}-\left(3x-1\right)$$

To find the opposite of 3x-1, find the opposite of each term.

$$9x^{2}-42x+49-5\left(2x+1\right)\left(x-2\right)=-x^{2}-3x+1$$

Add x^{2} to both sides.

$$9x^{2}-42x+49-5\left(2x+1\right)\left(x-2\right)+x^{2}=-3x+1$$

Add 3x to both sides.

$$9x^{2}-42x+49-5\left(2x+1\right)\left(x-2\right)+x^{2}+3x=1$$

Use the distributive property to multiply -5 by 2x+1.

$$9x^{2}-42x+49+\left(-10x-5\right)\left(x-2\right)+x^{2}+3x=1$$

Use the distributive property to multiply -10x-5 by x-2 and combine like terms.

$$9x^{2}-42x+49-10x^{2}+15x+10+x^{2}+3x=1$$

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

$$-x^{2}-42x+49+15x+10+x^{2}+3x=1$$

Combine -42x and 15x to get -27x.

$$-x^{2}-27x+49+10+x^{2}+3x=1$$

Add 49 and 10 to get 59.

$$-x^{2}-27x+59+x^{2}+3x=1$$

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

$$-27x+59+3x=1$$

Combine -27x and 3x to get -24x.

$$-24x+59=1$$

Subtract 59 from both sides.

$$-24x=1-59$$

Subtract 59 from 1 to get -58.

$$-24x=-58$$

Divide both sides by -24.

$$x=\frac{-58}{-24}$$

Reduce the fraction \frac{-58}{-24} to lowest terms by extracting and canceling out -2.

$$x=\frac{29}{12}$$