2x^3+x^2-18=x(2x^2+3)

Solution for 2x^3+x^2-18=x(2x^2+3) equation:

Simplifying
2x3 + x2 + -18 = x(2x2 + 3)

Reorder the terms:
-18 + x2 + 2x3 = x(2x2 + 3)

Reorder the terms:
-18 + x2 + 2x3 = x(3 + 2x2)
-18 + x2 + 2x3 = (3 * x + 2x2 * x)
-18 + x2 + 2x3 = (3x + 2x3)

Add '-2x3' to each side of the equation.
-18 + x2 + 2x3 + -2x3 = 3x + 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-18 + x2 + 0 = 3x + 2x3 + -2x3
-18 + x2 = 3x + 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-18 + x2 = 3x + 0
-18 + x2 = 3x

Solving
-18 + x2 = 3x

Solving for variable 'x'.

Reorder the terms:
-18 + -3x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-18 + -3x + x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3, 6}