(x+2)(x+3)=156

Solution for (x+2)(x+3)=156 equation:

Simplifying
(x + 2)(x + 3) = 156

Reorder the terms:
(2 + x)(x + 3) = 156

Reorder the terms:
(2 + x)(3 + x) = 156

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 156
((3 * 2 + x * 2) + x(3 + x)) = 156
((6 + 2x) + x(3 + x)) = 156
(6 + 2x + (3 * x + x * x)) = 156
(6 + 2x + (3x + x2)) = 156

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 156

Solving
6 + 5x + x2 = 156

Solving for variable 'x'.

Reorder the terms:
6 + -156 + 5x + x2 = 156 + -156

Combine like terms: 6 + -156 = -150
-150 + 5x + x2 = 156 + -156

Combine like terms: 156 + -156 = 0
-150 + 5x + x2 = 0

Factor a trinomial.
(-15 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-15, 10}