0=3x^2+3x-18

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Solution for 0=3x^2+3x-18 equation: 


Simplifying
0 = 3x2 + 3x + -18

Reorder the terms:
0 = -18 + 3x + 3x2

Solving
0 = -18 + 3x + 3x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -1x + -1x2) = 0

Factor a trinomial.
3((2 + -1x)(3 + x)) = 0

Ignore the factor 3.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {2, -3}

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