(x-3)(x-3)6=96

Solution for (x-3)(x-3)6=96 equation:

Simplifying
(x + -3)(x + -3) * 6 = 96

Reorder the terms:
(-3 + x)(x + -3) * 6 = 96

Reorder the terms:
(-3 + x)(-3 + x) * 6 = 96

Reorder the terms for easier multiplication:
6(-3 + x)(-3 + x) = 96

Multiply (-3 + x) * (-3 + x)
6(-3(-3 + x) + x(-3 + x)) = 96
6((-3 * -3 + x * -3) + x(-3 + x)) = 96
6((9 + -3x) + x(-3 + x)) = 96
6(9 + -3x + (-3 * x + x * x)) = 96
6(9 + -3x + (-3x + x2)) = 96

Combine like terms: -3x + -3x = -6x
6(9 + -6x + x2) = 96
(9 * 6 + -6x * 6 + x2 * 6) = 96
(54 + -36x + 6x2) = 96

Solving
54 + -36x + 6x2 = 96

Solving for variable 'x'.

Reorder the terms:
54 + -96 + -36x + 6x2 = 96 + -96

Combine like terms: 54 + -96 = -42
-42 + -36x + 6x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-42 + -36x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + -6x + x2) = 0

Factor a trinomial.
6((-1 + -1x)(7 + -1x)) = 0

Ignore the factor 6.
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 '(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 = {-1, 7}