3x^2=30x-72

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

Simplifying
3x2 = 30x + -72

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

Solving
3x2 = -72 + 30x

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
3((4 + -1x)(6 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {4, 6}