-2x^2+30x=72

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

Simplifying
-2x2 + 30x = 72

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

Solving
30x + -2x2 = 72

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 15x + -1x2) = 0

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

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

Simplifying
-12 + x = 0

Solving
-12 + x = 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 + x = 0 + 12

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

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

Simplifying
x = 12
Subproblem 2
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
Solution
x = {12, 3}