72=-3+3(x-1)(x-1)

Solution for 72=-3+3(x-1)(x-1) equation:

Simplifying
72 = -3 + 3(x + -1)(x + -1)

Reorder the terms:
72 = -3 + 3(-1 + x)(x + -1)

Reorder the terms:
72 = -3 + 3(-1 + x)(-1 + x)

Multiply (-1 + x) * (-1 + x)
72 = -3 + 3(-1(-1 + x) + x(-1 + x))
72 = -3 + 3((-1 * -1 + x * -1) + x(-1 + x))
72 = -3 + 3((1 + -1x) + x(-1 + x))
72 = -3 + 3(1 + -1x + (-1 * x + x * x))
72 = -3 + 3(1 + -1x + (-1x + x2))

Combine like terms: -1x + -1x = -2x
72 = -3 + 3(1 + -2x + x2)
72 = -3 + (1 * 3 + -2x * 3 + x2 * 3)
72 = -3 + (3 + -6x + 3x2)

Combine like terms: -3 + 3 = 0
72 = 0 + -6x + 3x2
72 = -6x + 3x2

Solving
72 = -6x + 3x2

Solving for variable 'x'.

Reorder the terms:
72 + 6x + -3x2 = -6x + 6x + 3x2 + -3x2

Combine like terms: -6x + 6x = 0
72 + 6x + -3x2 = 0 + 3x2 + -3x2
72 + 6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
72 + 6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 2x + -1x2) = 0

Factor a trinomial.
3((6 + -1x)(4 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {6, -4}