6x^2-30x=144

Solution for 6x^2-30x=144 equation:

Simplifying
6x2 + -30x = 144

Reorder the terms:
-30x + 6x2 = 144

Solving
-30x + 6x2 = 144

Solving for variable 'x'.

Reorder the terms:
-144 + -30x + 6x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + -30x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-24 + -5x + x2) = 0

Factor a trinomial.
6((-3 + -1x)(8 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3, 8}