4(x^2-4)=(x+10)(x+2)

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Solution for 4(x^2-4)=(x+10)(x+2) equation: 


Simplifying
4(x2 + -4) = (x + 10)(x + 2)

Reorder the terms:
4(-4 + x2) = (x + 10)(x + 2)
(-4 * 4 + x2 * 4) = (x + 10)(x + 2)
(-16 + 4x2) = (x + 10)(x + 2)

Reorder the terms:
-16 + 4x2 = (10 + x)(x + 2)

Reorder the terms:
-16 + 4x2 = (10 + x)(2 + x)

Multiply (10 + x) * (2 + x)
-16 + 4x2 = (10(2 + x) + x(2 + x))
-16 + 4x2 = ((2 * 10 + x * 10) + x(2 + x))
-16 + 4x2 = ((20 + 10x) + x(2 + x))
-16 + 4x2 = (20 + 10x + (2 * x + x * x))
-16 + 4x2 = (20 + 10x + (2x + x2))

Combine like terms: 10x + 2x = 12x
-16 + 4x2 = (20 + 12x + x2)

Solving
-16 + 4x2 = 20 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
-16 + -20 + -12x + 4x2 + -1x2 = 20 + 12x + x2 + -20 + -12x + -1x2

Combine like terms: -16 + -20 = -36
-36 + -12x + 4x2 + -1x2 = 20 + 12x + x2 + -20 + -12x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-36 + -12x + 3x2 = 20 + 12x + x2 + -20 + -12x + -1x2

Reorder the terms:
-36 + -12x + 3x2 = 20 + -20 + 12x + -12x + x2 + -1x2

Combine like terms: 20 + -20 = 0
-36 + -12x + 3x2 = 0 + 12x + -12x + x2 + -1x2
-36 + -12x + 3x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
-36 + -12x + 3x2 = 0 + x2 + -1x2
-36 + -12x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -4x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(6 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 6}

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