(x+4)*(x-1)=2x(x+4)

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Solution for (x+4)*(x-1)=2x(x+4) equation: 


Simplifying
(x + 4)(x + -1) = 2x(x + 4)

Reorder the terms:
(4 + x)(x + -1) = 2x(x + 4)

Reorder the terms:
(4 + x)(-1 + x) = 2x(x + 4)

Multiply (4 + x) * (-1 + x)
(4(-1 + x) + x(-1 + x)) = 2x(x + 4)
((-1 * 4 + x * 4) + x(-1 + x)) = 2x(x + 4)
((-4 + 4x) + x(-1 + x)) = 2x(x + 4)
(-4 + 4x + (-1 * x + x * x)) = 2x(x + 4)
(-4 + 4x + (-1x + x2)) = 2x(x + 4)

Combine like terms: 4x + -1x = 3x
(-4 + 3x + x2) = 2x(x + 4)

Reorder the terms:
-4 + 3x + x2 = 2x(4 + x)
-4 + 3x + x2 = (4 * 2x + x * 2x)
-4 + 3x + x2 = (8x + 2x2)

Solving
-4 + 3x + x2 = 8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + 3x + -8x + x2 + -2x2 = 8x + 2x2 + -8x + -2x2

Combine like terms: 3x + -8x = -5x
-4 + -5x + x2 + -2x2 = 8x + 2x2 + -8x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-4 + -5x + -1x2 = 8x + 2x2 + -8x + -2x2

Reorder the terms:
-4 + -5x + -1x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
-4 + -5x + -1x2 = 0 + 2x2 + -2x2
-4 + -5x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + -5x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 5x + x2) = 0

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

Ignore the factor -1.

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-4, -1}

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