x^2+7x+12=72

Solution for x^2+7x+12=72 equation:

Simplifying
x2 + 7x + 12 = 72

Reorder the terms:
12 + 7x + x2 = 72

Solving
12 + 7x + x2 = 72

Solving for variable 'x'.

Reorder the terms:
12 + -72 + 7x + x2 = 72 + -72

Combine like terms: 12 + -72 = -60
-60 + 7x + x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-60 + 7x + x2 = 0

Factor a trinomial.
(-12 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-12, 5}