Solve (x-3)(x^2+3x+9)-(3x-17)=x^3-12

$$(x-3)( { x }^{ 2 } +3x+9)-(3x-17)= { x }^{ 3 } -12$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-3 by x^{2}+3x+9 and combine like terms.

$$x^{3}-27-\left(3x-17\right)=x^{3}-12$$

To find the opposite of 3x-17, find the opposite of each term.

$$x^{3}-27-3x+17=x^{3}-12$$

Add -27 and 17 to get -10.

$$x^{3}-10-3x=x^{3}-12$$

Subtract x^{3} from both sides.

$$x^{3}-10-3x-x^{3}=-12$$

Combine x^{3} and -x^{3} to get 0.

$$-10-3x=-12$$

Add 10 to both sides.

$$-3x=-12+10$$

Add -12 and 10 to get -2.

$$-3x=-2$$

Divide both sides by -3.

$$x=\frac{-2}{-3}$$

Fraction \frac{-2}{-3} can be simplified to \frac{2}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{2}{3}$$