56=(x+4)(x+5)

Solution for 56=(x+4)(x+5) equation:

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

Reorder the terms:
56 = (4 + x)(x + 5)

Reorder the terms:
56 = (4 + x)(5 + x)

Multiply (4 + x) * (5 + x)
56 = (4(5 + x) + x(5 + x))
56 = ((5 * 4 + x * 4) + x(5 + x))
56 = ((20 + 4x) + x(5 + x))
56 = (20 + 4x + (5 * x + x * x))
56 = (20 + 4x + (5x + x2))

Combine like terms: 4x + 5x = 9x
56 = (20 + 9x + x2)

Solving
56 = 20 + 9x + x2

Solving for variable 'x'.

Combine like terms: 56 + -20 = 36
36 + -9x + -1x2 = 20 + 9x + x2 + -20 + -9x + -1x2

Reorder the terms:
36 + -9x + -1x2 = 20 + -20 + 9x + -9x + x2 + -1x2

Combine like terms: 20 + -20 = 0
36 + -9x + -1x2 = 0 + 9x + -9x + x2 + -1x2
36 + -9x + -1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
36 + -9x + -1x2 = 0 + x2 + -1x2
36 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
36 + -9x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(12 + x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
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 = {3, -12}