=(x+5)(x+4)

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

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

Reorder the terms:
0 = (5 + x)(x + 4)

Reorder the terms:
0 = (5 + x)(4 + x)

Multiply (5 + x) * (4 + x)
0 = (5(4 + x) + x(4 + x))
0 = ((4 * 5 + x * 5) + x(4 + x))
0 = ((20 + 5x) + x(4 + x))
0 = (20 + 5x + (4 * x + x * x))
0 = (20 + 5x + (4x + x2))

Combine like terms: 5x + 4x = 9x
0 = (20 + 9x + x2)

Solving
0 = 20 + 9x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(20 + 9x + x2) = 0

Factor a trinomial.
-1((5 + x)(4 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-5, -4}