(x+4)(x+5)=72

Solution for (x+4)(x+5)=72 equation:

Simplifying
(x + 4)(x + 5) = 72

Reorder the terms:
(4 + x)(x + 5) = 72

Reorder the terms:
(4 + x)(5 + x) = 72

Multiply (4 + x) * (5 + x)
(4(5 + x) + x(5 + x)) = 72
((5 * 4 + x * 4) + x(5 + x)) = 72
((20 + 4x) + x(5 + x)) = 72
(20 + 4x + (5 * x + x * x)) = 72
(20 + 4x + (5x + x2)) = 72

Combine like terms: 4x + 5x = 9x
(20 + 9x + x2) = 72

Solving
20 + 9x + x2 = 72

Solving for variable 'x'.

Reorder the terms:
20 + -72 + 9x + x2 = 72 + -72

Combine like terms: 20 + -72 = -52
-52 + 9x + x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-52 + 9x + x2 = 0

Factor a trinomial.
(-13 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
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 = {-13, 4}