(12x^2)-(18x)-30=0

Solution for (12x^2)-(18x)-30=0 equation:

Simplifying
(12x2) + -1(18x) + -30 = 0

Remove parenthesis around (18x)
(12x2) + -1 * 18x + -30 = 0

Multiply -1 * 18
(12x2) + -18x + -30 = 0

Reorder the terms:
-30 + -18x + (12x2) = 0

Solving
-30 + -18x + (12x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + -3x + (2x2)) = 0

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

Ignore the factor 6.
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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-1, 2.5}