3(x-5)(x-5)+6=54

Solution for 3(x-5)(x-5)+6=54 equation:

Simplifying
3(x + -5)(x + -5) + 6 = 54

Reorder the terms:
3(-5 + x)(x + -5) + 6 = 54

Reorder the terms:
3(-5 + x)(-5 + x) + 6 = 54

Multiply (-5 + x) * (-5 + x)
3(-5(-5 + x) + x(-5 + x)) + 6 = 54
3((-5 * -5 + x * -5) + x(-5 + x)) + 6 = 54
3((25 + -5x) + x(-5 + x)) + 6 = 54
3(25 + -5x + (-5 * x + x * x)) + 6 = 54
3(25 + -5x + (-5x + x2)) + 6 = 54

Combine like terms: -5x + -5x = -10x
3(25 + -10x + x2) + 6 = 54
(25 * 3 + -10x * 3 + x2 * 3) + 6 = 54
(75 + -30x + 3x2) + 6 = 54

Reorder the terms:
75 + 6 + -30x + 3x2 = 54

Combine like terms: 75 + 6 = 81
81 + -30x + 3x2 = 54

Solving
81 + -30x + 3x2 = 54

Solving for variable 'x'.

Reorder the terms:
81 + -54 + -30x + 3x2 = 54 + -54

Combine like terms: 81 + -54 = 27
27 + -30x + 3x2 = 54 + -54

Combine like terms: 54 + -54 = 0
27 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -10x + x2) = 0

Factor a trinomial.
3((1 + -1x)(9 + -1x)) = 0

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {1, 9}