4*(5-2*x)(5-2*x)-16=0

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Solution for 4*(5-2*x)(5-2*x)-16=0 equation: 


Simplifying
4(5 + -2x)(5 + -2x) + -16 = 0

Multiply (5 + -2x) * (5 + -2x)
4(5(5 + -2x) + -2x * (5 + -2x)) + -16 = 0
4((5 * 5 + -2x * 5) + -2x * (5 + -2x)) + -16 = 0
4((25 + -10x) + -2x * (5 + -2x)) + -16 = 0
4(25 + -10x + (5 * -2x + -2x * -2x)) + -16 = 0
4(25 + -10x + (-10x + 4x2)) + -16 = 0

Combine like terms: -10x + -10x = -20x
4(25 + -20x + 4x2) + -16 = 0
(25 * 4 + -20x * 4 + 4x2 * 4) + -16 = 0
(100 + -80x + 16x2) + -16 = 0

Reorder the terms:
100 + -16 + -80x + 16x2 = 0

Combine like terms: 100 + -16 = 84
84 + -80x + 16x2 = 0

Solving
84 + -80x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + -20x + 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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