72=(x+3)(x+4)

Solution for 72=(x+3)(x+4) equation:

Simplifying
72 = (x + 3)(x + 4)

Reorder the terms:
72 = (3 + x)(x + 4)

Reorder the terms:
72 = (3 + x)(4 + x)

Multiply (3 + x) * (4 + x)
72 = (3(4 + x) + x(4 + x))
72 = ((4 * 3 + x * 3) + x(4 + x))
72 = ((12 + 3x) + x(4 + x))
72 = (12 + 3x + (4 * x + x * x))
72 = (12 + 3x + (4x + x2))

Combine like terms: 3x + 4x = 7x
72 = (12 + 7x + x2)

Solving
72 = 12 + 7x + x2

Solving for variable 'x'.

Combine like terms: 72 + -12 = 60
60 + -7x + -1x2 = 12 + 7x + x2 + -12 + -7x + -1x2

Reorder the terms:
60 + -7x + -1x2 = 12 + -12 + 7x + -7x + x2 + -1x2

Combine like terms: 12 + -12 = 0
60 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2
60 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
60 + -7x + -1x2 = 0 + x2 + -1x2
60 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + -7x + -1x2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 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 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

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