2x^2+32x=72

Solution for 2x^2+32x=72 equation:

Simplifying
2x2 + 32x = 72

Reorder the terms:
32x + 2x2 = 72

Solving
32x + 2x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + 32x + 2x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 32x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 16x + x2) = 0

Factor a trinomial.
2((-18 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18
Subproblem 2
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
Solution
x = {-18, 2}