0=(x+4)(-2x-5)

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Solution for 0=(x+4)(-2x-5) equation: 


Simplifying
0 = (x + 4)(-2x + -5)

Reorder the terms:
0 = (4 + x)(-2x + -5)

Reorder the terms:
0 = (4 + x)(-5 + -2x)

Multiply (4 + x) * (-5 + -2x)
0 = (4(-5 + -2x) + x(-5 + -2x))
0 = ((-5 * 4 + -2x * 4) + x(-5 + -2x))
0 = ((-20 + -8x) + x(-5 + -2x))
0 = (-20 + -8x + (-5 * x + -2x * x))
0 = (-20 + -8x + (-5x + -2x2))

Combine like terms: -8x + -5x = -13x
0 = (-20 + -13x + -2x2)

Solving
0 = -20 + -13x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + 13x + 2x2 = -20 + -13x + -2x2 + 20 + 13x + 2x2

Reorder the terms:
20 + 13x + 2x2 = -20 + 20 + -13x + 13x + -2x2 + 2x2

Combine like terms: -20 + 20 = 0
20 + 13x + 2x2 = 0 + -13x + 13x + -2x2 + 2x2
20 + 13x + 2x2 = -13x + 13x + -2x2 + 2x2

Combine like terms: -13x + 13x = 0
20 + 13x + 2x2 = 0 + -2x2 + 2x2
20 + 13x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
20 + 13x + 2x2 = 0

Factor a trinomial.
(4 + x)(5 + 2x) = 0


Subproblem 1
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

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

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {-4, -2.5}

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