Solve (x-3)(x+3)=3(x-1)/2+x^2

$$( x - 3 ) ( x + 3 ) = \frac { 3 ( x - 1 ) } { 2 } + x ^ { 2 }$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

Use the distributive property to multiply 2 by x-3.

$$\left(2x-6\right)\left(x+3\right)=3\left(x-1\right)+2x^{2}$$

Use the distributive property to multiply 2x-6 by x+3 and combine like terms.

$$2x^{2}-18=3\left(x-1\right)+2x^{2}$$

Use the distributive property to multiply 3 by x-1.

$$2x^{2}-18=3x-3+2x^{2}$$

Subtract 3x from both sides.

$$2x^{2}-18-3x=-3+2x^{2}$$

Subtract 2x^{2} from both sides.

$$2x^{2}-18-3x-2x^{2}=-3$$

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

$$-18-3x=-3$$

Add 18 to both sides.

$$-3x=-3+18$$

Add -3 and 18 to get 15.

$$-3x=15$$

Divide both sides by -3.

$$x=\frac{15}{-3}$$

Divide 15 by -3 to get -5.

$$x=-5$$