3(x-5)(x-5)=27

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Solution for 3(x-5)(x-5)=27 equation: 


Simplifying
3(x + -5)(x + -5) = 27

Reorder the terms:
3(-5 + x)(x + -5) = 27

Reorder the terms:
3(-5 + x)(-5 + x) = 27

Multiply (-5 + x) * (-5 + x)
3(-5(-5 + x) + x(-5 + x)) = 27
3((-5 * -5 + x * -5) + x(-5 + x)) = 27
3((25 + -5x) + x(-5 + x)) = 27
3(25 + -5x + (-5 * x + x * x)) = 27
3(25 + -5x + (-5x + x2)) = 27

Combine like terms: -5x + -5x = -10x
3(25 + -10x + x2) = 27
(25 * 3 + -10x * 3 + x2 * 3) = 27
(75 + -30x + 3x2) = 27

Solving
75 + -30x + 3x2 = 27

Solving for variable 'x'.

Reorder the terms:
75 + -27 + -30x + 3x2 = 27 + -27

Combine like terms: 75 + -27 = 48
48 + -30x + 3x2 = 27 + -27

Combine like terms: 27 + -27 = 0
48 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + -10x + x2) = 0

Factor a trinomial.
3((2 + -1x)(8 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {2, 8}

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