8=2(x-3)(x-3)

Solution for 8=2(x-3)(x-3) equation:

Simplifying
8 = 2(x + -3)(x + -3)

Reorder the terms:
8 = 2(-3 + x)(x + -3)

Reorder the terms:
8 = 2(-3 + x)(-3 + x)

Multiply (-3 + x) * (-3 + x)
8 = 2(-3(-3 + x) + x(-3 + x))
8 = 2((-3 * -3 + x * -3) + x(-3 + x))
8 = 2((9 + -3x) + x(-3 + x))
8 = 2(9 + -3x + (-3 * x + x * x))
8 = 2(9 + -3x + (-3x + x2))

Combine like terms: -3x + -3x = -6x
8 = 2(9 + -6x + x2)
8 = (9 * 2 + -6x * 2 + x2 * 2)
8 = (18 + -12x + 2x2)

Solving
8 = 18 + -12x + 2x2

Solving for variable 'x'.

Combine like terms: 8 + -18 = -10
-10 + 12x + -2x2 = 18 + -12x + 2x2 + -18 + 12x + -2x2

Reorder the terms:
-10 + 12x + -2x2 = 18 + -18 + -12x + 12x + 2x2 + -2x2

Combine like terms: 18 + -18 = 0
-10 + 12x + -2x2 = 0 + -12x + 12x + 2x2 + -2x2
-10 + 12x + -2x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
-10 + 12x + -2x2 = 0 + 2x2 + -2x2
-10 + 12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + 12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 6x + -1x2) = 0

Factor a trinomial.
2((-5 + x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 2
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
Solution
x = {5, 1}