-6x^2+87x-117=0

Solution for -6x^2+87x-117=0 equation:

Simplifying
-6x2 + 87x + -117 = 0

Reorder the terms:
-117 + 87x + -6x2 = 0

Solving
-117 + 87x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-39 + 29x + -2x2) = 0

Factor a trinomial.
3((-13 + x)(3 + -2x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-13 + x)' equal to zero and attempt to solve:

Simplifying
-13 + x = 0

Solving
-13 + x = 0

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

Add '13' to each side of the equation.
-13 + 13 + x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + x = 0 + 13
x = 0 + 13

Combine like terms: 0 + 13 = 13
x = 13

Simplifying
x = 13
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {13, 1.5}