(3x-5)(3x-5)-16=0

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Solution for (3x-5)(3x-5)-16=0 equation: 


Simplifying
(3x + -5)(3x + -5) + -16 = 0

Reorder the terms:
(-5 + 3x)(3x + -5) + -16 = 0

Reorder the terms:
(-5 + 3x)(-5 + 3x) + -16 = 0

Multiply (-5 + 3x) * (-5 + 3x)
(-5(-5 + 3x) + 3x * (-5 + 3x)) + -16 = 0
((-5 * -5 + 3x * -5) + 3x * (-5 + 3x)) + -16 = 0
((25 + -15x) + 3x * (-5 + 3x)) + -16 = 0
(25 + -15x + (-5 * 3x + 3x * 3x)) + -16 = 0
(25 + -15x + (-15x + 9x2)) + -16 = 0

Combine like terms: -15x + -15x = -30x
(25 + -30x + 9x2) + -16 = 0

Reorder the terms:
25 + -16 + -30x + 9x2 = 0

Combine like terms: 25 + -16 = 9
9 + -30x + 9x2 = 0

Solving
9 + -30x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -10x + 3x2) = 0

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

Ignore the factor 3.

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
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
Solution
x = {0.3333333333, 3}

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