x^2-16=(2x-1)(x+4)

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Solution for x^2-16=(2x-1)(x+4) equation: 


Simplifying
x2 + -16 = (2x + -1)(x + 4)

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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -16 + 4 = -12
-12 + -7x + x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-12 + -7x + -1x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2

Reorder the terms:
-12 + -7x + -1x2 = -4 + 4 + 7x + -7x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
-12 + -7x + -1x2 = 0 + 7x + -7x + 2x2 + -2x2
-12 + -7x + -1x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
-12 + -7x + -1x2 = 0 + 2x2 + -2x2
-12 + -7x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 7x + x2) = 0

Factor a trinomial.
-1((4 + x)(3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-4, -3}

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