4(3x-5)(3x-5)=0

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Solution for 4(3x-5)(3x-5)=0 equation: 


Simplifying
4(3x + -5)(3x + -5) = 0

Reorder the terms:
4(-5 + 3x)(3x + -5) = 0

Reorder the terms:
4(-5 + 3x)(-5 + 3x) = 0

Multiply (-5 + 3x) * (-5 + 3x)
4(-5(-5 + 3x) + 3x * (-5 + 3x)) = 0
4((-5 * -5 + 3x * -5) + 3x * (-5 + 3x)) = 0
4((25 + -15x) + 3x * (-5 + 3x)) = 0
4(25 + -15x + (-5 * 3x + 3x * 3x)) = 0
4(25 + -15x + (-15x + 9x2)) = 0

Combine like terms: -15x + -15x = -30x
4(25 + -30x + 9x2) = 0
(25 * 4 + -30x * 4 + 9x2 * 4) = 0
(100 + -120x + 36x2) = 0

Solving
100 + -120x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + -30x + 9x2) = 0

Factor a trinomial.
4((5 + -3x)(5 + -3x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {1.666666667, 1.666666667}

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