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

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


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

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

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

Multiply (4 + x) * (4 + x)
(4(4 + x) + x(4 + x)) = (2x + -1)(x + 4)
((4 * 4 + x * 4) + x(4 + x)) = (2x + -1)(x + 4)
((16 + 4x) + x(4 + x)) = (2x + -1)(x + 4)
(16 + 4x + (4 * x + x * x)) = (2x + -1)(x + 4)
(16 + 4x + (4x + x2)) = (2x + -1)(x + 4)

Combine like terms: 4x + 4x = 8x
(16 + 8x + x2) = (2x + -1)(x + 4)

Reorder the terms:
16 + 8x + x2 = (-1 + 2x)(x + 4)

Reorder the terms:
16 + 8x + x2 = (-1 + 2x)(4 + x)

Multiply (-1 + 2x) * (4 + x)
16 + 8x + x2 = (-1(4 + x) + 2x * (4 + x))
16 + 8x + x2 = ((4 * -1 + x * -1) + 2x * (4 + x))
16 + 8x + x2 = ((-4 + -1x) + 2x * (4 + x))
16 + 8x + x2 = (-4 + -1x + (4 * 2x + x * 2x))
16 + 8x + x2 = (-4 + -1x + (8x + 2x2))

Combine like terms: -1x + 8x = 7x
16 + 8x + x2 = (-4 + 7x + 2x2)

Solving
16 + 8x + x2 = -4 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
16 + 4 + 8x + -7x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: 16 + 4 = 20
20 + 8x + -7x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: 8x + -7x = 1x
20 + 1x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: x2 + -2x2 = -1x2
20 + 1x + -1x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Reorder the terms:
20 + 1x + -1x2 = -4 + 4 + 7x + -7x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
20 + 1x + -1x2 = 0 + 7x + -7x + 2x2 + -2x2
20 + 1x + -1x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
20 + 1x + -1x2 = 0 + 2x2 + -2x2
20 + 1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + 1x + -1x2 = 0

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


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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
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}

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