((-6x^2)+18x+60)=0

Solution for ((-6x^2)+18x+60)=0 equation:

Simplifying
((-6x2) + 18x + 60) = 0

Reorder the terms:
(60 + 18x + (-6x2)) = 0

Remove parenthesis around (60 + 18x + (-6x2))
60 + 18x + (-6x2) = 0

Solving
60 + 18x + (-6x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(10 + 3x + (-1x2)) = 0

Factor a trinomial.
6((5 + -1x)(2 + x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {5, -2}