2x^2+10x=72

Solution for 2x^2+10x=72 equation:

Simplifying
2x2 + 10x = 72

Reorder the terms:
10x + 2x2 = 72

Solving
10x + 2x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + 10x + 2x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 5x + x2) = 0

Factor a trinomial.
2((-9 + -1x)(4 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 4}