2x^2=30x-72

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

Simplifying
2x2 = 30x + -72

Reorder the terms:
2x2 = -72 + 30x

Solving
2x2 = -72 + 30x

Solving for variable 'x'.

Reorder the terms:
72 + -30x + 2x2 = -72 + 30x + 72 + -30x

Reorder the terms:
72 + -30x + 2x2 = -72 + 72 + 30x + -30x

Combine like terms: -72 + 72 = 0
72 + -30x + 2x2 = 0 + 30x + -30x
72 + -30x + 2x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
72 + -30x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -15x + x2) = 0

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

Ignore the factor 2.
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 '(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 = {3, 12}