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

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

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

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

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

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

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

Solving
20 + 9x + x2 = 56

Solving for variable 'x'.

Reorder the terms:
20 + -56 + 9x + x2 = 56 + -56

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

Combine like terms: 56 + -56 = 0
-36 + 9x + x2 = 0

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

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

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 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 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
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
Solution
x = {-12, 3}