(4x+2)(2x-4)=100

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Solution for (4x+2)(2x-4)=100 equation: 


Simplifying
(4x + 2)(2x + -4) = 100

Reorder the terms:
(2 + 4x)(2x + -4) = 100

Reorder the terms:
(2 + 4x)(-4 + 2x) = 100

Multiply (2 + 4x) * (-4 + 2x)
(2(-4 + 2x) + 4x * (-4 + 2x)) = 100
((-4 * 2 + 2x * 2) + 4x * (-4 + 2x)) = 100
((-8 + 4x) + 4x * (-4 + 2x)) = 100
(-8 + 4x + (-4 * 4x + 2x * 4x)) = 100
(-8 + 4x + (-16x + 8x2)) = 100

Combine like terms: 4x + -16x = -12x
(-8 + -12x + 8x2) = 100

Solving
-8 + -12x + 8x2 = 100

Solving for variable 'x'.

Reorder the terms:
-8 + -100 + -12x + 8x2 = 100 + -100

Combine like terms: -8 + -100 = -108
-108 + -12x + 8x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-108 + -12x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + -3x + 2x2) = 0

Factor a trinomial.
4((-3 + -1x)(9 + -2x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-3, 4.5}

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