0=2x^2+24x+72

Solution for 0=2x^2+24x+72 equation:

Simplifying
0 = 2x2 + 24x + 72

Reorder the terms:
0 = 72 + 24x + 2x2

Solving
0 = 72 + 24x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -72 = -72
-72 + -24x + -2x2 = 72 + 24x + 2x2 + -72 + -24x + -2x2

Reorder the terms:
-72 + -24x + -2x2 = 72 + -72 + 24x + -24x + 2x2 + -2x2

Combine like terms: 72 + -72 = 0
-72 + -24x + -2x2 = 0 + 24x + -24x + 2x2 + -2x2
-72 + -24x + -2x2 = 24x + -24x + 2x2 + -2x2

Combine like terms: 24x + -24x = 0
-72 + -24x + -2x2 = 0 + 2x2 + -2x2
-72 + -24x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-72 + -24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(36 + 12x + x2) = 0

Factor a trinomial.
-2((6 + x)(6 + x)) = 0

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

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

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

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

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