72=(x+6)(x+7)

Solution for 72=(x+6)(x+7) equation:

Simplifying
72 = (x + 6)(x + 7)

Reorder the terms:
72 = (6 + x)(x + 7)

Reorder the terms:
72 = (6 + x)(7 + x)

Multiply (6 + x) * (7 + x)
72 = (6(7 + x) + x(7 + x))
72 = ((7 * 6 + x * 6) + x(7 + x))
72 = ((42 + 6x) + x(7 + x))
72 = (42 + 6x + (7 * x + x * x))
72 = (42 + 6x + (7x + x2))

Combine like terms: 6x + 7x = 13x
72 = (42 + 13x + x2)

Solving
72 = 42 + 13x + x2

Solving for variable 'x'.

Combine like terms: 72 + -42 = 30
30 + -13x + -1x2 = 42 + 13x + x2 + -42 + -13x + -1x2

Reorder the terms:
30 + -13x + -1x2 = 42 + -42 + 13x + -13x + x2 + -1x2

Combine like terms: 42 + -42 = 0
30 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2
30 + -13x + -1x2 = 13x + -13x + x2 + -1x2

Combine like terms: 13x + -13x = 0
30 + -13x + -1x2 = 0 + x2 + -1x2
30 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + -13x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(15 + x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

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

Simplifying
15 + x = 0

Solving
15 + x = 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 + x = 0 + -15

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

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

Simplifying
x = -15
Solution
x = {2, -15}