(x+4)(x-1)=-5x-4

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Solution for (x+4)(x-1)=-5x-4 equation: 


Simplifying
(x + 4)(x + -1) = -5x + -4

Reorder the terms:
(4 + x)(x + -1) = -5x + -4

Reorder the terms:
(4 + x)(-1 + x) = -5x + -4

Multiply (4 + x) * (-1 + x)
(4(-1 + x) + x(-1 + x)) = -5x + -4
((-1 * 4 + x * 4) + x(-1 + x)) = -5x + -4
((-4 + 4x) + x(-1 + x)) = -5x + -4
(-4 + 4x + (-1 * x + x * x)) = -5x + -4
(-4 + 4x + (-1x + x2)) = -5x + -4

Combine like terms: 4x + -1x = 3x
(-4 + 3x + x2) = -5x + -4

Reorder the terms:
-4 + 3x + x2 = -4 + -5x

Add '4' to each side of the equation.
-4 + 3x + 4 + x2 = -4 + 4 + -5x

Reorder the terms:
-4 + 4 + 3x + x2 = -4 + 4 + -5x

Combine like terms: -4 + 4 = 0
0 + 3x + x2 = -4 + 4 + -5x
3x + x2 = -4 + 4 + -5x

Combine like terms: -4 + 4 = 0
3x + x2 = 0 + -5x
3x + x2 = -5x

Solving
3x + x2 = -5x

Solving for variable 'x'.

Reorder the terms:
3x + 5x + x2 = -5x + 5x

Combine like terms: 3x + 5x = 8x
8x + x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
8x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {0, -8}

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