3x^2-30x=72

Solution for 3x^2-30x=72 equation:

Simplifying
3x2 + -30x = 72

Reorder the terms:
-30x + 3x2 = 72

Solving
-30x + 3x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + -30x + 3x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -10x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(12 + -1x)) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-2, 12}