3x^2=15x+18

Solution for 3x^2=15x+18 equation:

Simplifying
3x2 = 15x + 18

Reorder the terms:
3x2 = 18 + 15x

Solving
3x2 = 18 + 15x

Solving for variable 'x'.

Reorder the terms:
-18 + -15x + 3x2 = 18 + 15x + -18 + -15x

Reorder the terms:
-18 + -15x + 3x2 = 18 + -18 + 15x + -15x

Combine like terms: 18 + -18 = 0
-18 + -15x + 3x2 = 0 + 15x + -15x
-18 + -15x + 3x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-18 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -5x + x2) = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
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 = {-1, 6}