3(x-5)(x-5)=12

Solution for 3(x-5)(x-5)=12 equation:

Simplifying
3(x + -5)(x + -5) = 12

Reorder the terms:
3(-5 + x)(x + -5) = 12

Reorder the terms:
3(-5 + x)(-5 + x) = 12

Multiply (-5 + x) * (-5 + x)
3(-5(-5 + x) + x(-5 + x)) = 12
3((-5 * -5 + x * -5) + x(-5 + x)) = 12
3((25 + -5x) + x(-5 + x)) = 12
3(25 + -5x + (-5 * x + x * x)) = 12
3(25 + -5x + (-5x + x2)) = 12

Combine like terms: -5x + -5x = -10x
3(25 + -10x + x2) = 12
(25 * 3 + -10x * 3 + x2 * 3) = 12
(75 + -30x + 3x2) = 12

Solving
75 + -30x + 3x2 = 12

Solving for variable 'x'.

Reorder the terms:
75 + -12 + -30x + 3x2 = 12 + -12

Combine like terms: 75 + -12 = 63
63 + -30x + 3x2 = 12 + -12

Combine like terms: 12 + -12 = 0
63 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + -10x + x2) = 0

Factor a trinomial.
3((3 + -1x)(7 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {3, 7}