(3x-5)(3x-5)=25

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Solution for (3x-5)(3x-5)=25 equation: 


Simplifying
(3x + -5)(3x + -5) = 25

Reorder the terms:
(-5 + 3x)(3x + -5) = 25

Reorder the terms:
(-5 + 3x)(-5 + 3x) = 25

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

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

Add '-25' to each side of the equation.
25 + -30x + -25 + 9x2 = 25 + -25

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

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

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

Solving
-30x + 9x2 = 0

Solving for variable 'x'.

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

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-10 + 3x)' equal to zero and attempt to solve:

Simplifying
-10 + 3x = 0

Solving
-10 + 3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + 3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3x = 0 + 10
3x = 0 + 10

Combine like terms: 0 + 10 = 10
3x = 10

Divide each side by '3'.
x = 3.333333333

Simplifying
x = 3.333333333
Solution
x = {0, 3.333333333}

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