(-2x+20)(-2x+16)=96

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Solution for (-2x+20)(-2x+16)=96 equation: 


Simplifying
(-2x + 20)(-2x + 16) = 96

Reorder the terms:
(20 + -2x)(-2x + 16) = 96

Reorder the terms:
(20 + -2x)(16 + -2x) = 96

Multiply (20 + -2x) * (16 + -2x)
(20(16 + -2x) + -2x * (16 + -2x)) = 96
((16 * 20 + -2x * 20) + -2x * (16 + -2x)) = 96
((320 + -40x) + -2x * (16 + -2x)) = 96
(320 + -40x + (16 * -2x + -2x * -2x)) = 96
(320 + -40x + (-32x + 4x2)) = 96

Combine like terms: -40x + -32x = -72x
(320 + -72x + 4x2) = 96

Solving
320 + -72x + 4x2 = 96

Solving for variable 'x'.

Reorder the terms:
320 + -96 + -72x + 4x2 = 96 + -96

Combine like terms: 320 + -96 = 224
224 + -72x + 4x2 = 96 + -96

Combine like terms: 96 + -96 = 0
224 + -72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(56 + -18x + x2) = 0

Factor a trinomial.
4((4 + -1x)(14 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {4, 14}

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