(5x-16)*(5x-16)=16

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Solution for (5x-16)*(5x-16)=16 equation: 


Simplifying
(5x + -16)(5x + -16) = 16

Reorder the terms:
(-16 + 5x)(5x + -16) = 16

Reorder the terms:
(-16 + 5x)(-16 + 5x) = 16

Multiply (-16 + 5x) * (-16 + 5x)
(-16(-16 + 5x) + 5x * (-16 + 5x)) = 16
((-16 * -16 + 5x * -16) + 5x * (-16 + 5x)) = 16
((256 + -80x) + 5x * (-16 + 5x)) = 16
(256 + -80x + (-16 * 5x + 5x * 5x)) = 16
(256 + -80x + (-80x + 25x2)) = 16

Combine like terms: -80x + -80x = -160x
(256 + -160x + 25x2) = 16

Solving
256 + -160x + 25x2 = 16

Solving for variable 'x'.

Reorder the terms:
256 + -16 + -160x + 25x2 = 16 + -16

Combine like terms: 256 + -16 = 240
240 + -160x + 25x2 = 16 + -16

Combine like terms: 16 + -16 = 0
240 + -160x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(48 + -32x + 5x2) = 0

Factor a trinomial.
5((12 + -5x)(4 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(12 + -5x)' equal to zero and attempt to solve:

Simplifying
12 + -5x = 0

Solving
12 + -5x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -5x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5x = 0 + -12
-5x = 0 + -12

Combine like terms: 0 + -12 = -12
-5x = -12

Divide each side by '-5'.
x = 2.4

Simplifying
x = 2.4

Subproblem 2
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
Solution
x = {2.4, 4}

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