2(4x-8)2x=84

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Solution for 2(4x-8)2x=84 equation: 


Simplifying
2(4x + -8) * 2x = 84

Reorder the terms:
2(-8 + 4x) * 2x = 84

Reorder the terms for easier multiplication:
2 * 2x(-8 + 4x) = 84

Multiply 2 * 2
4x(-8 + 4x) = 84
(-8 * 4x + 4x * 4x) = 84
(-32x + 16x2) = 84

Solving
-32x + 16x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + -32x + 16x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -32x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + -8x + 4x2) = 0

Factor a trinomial.
4((-3 + -2x)(7 + -2x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-1.5, 3.5}

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