2*(x-3)(x-3)+18=24

Solution for 2*(x-3)(x-3)+18=24 equation:

Simplifying
2(x + -3)(x + -3) + 18 = 24

Reorder the terms:
2(-3 + x)(x + -3) + 18 = 24

Reorder the terms:
2(-3 + x)(-3 + x) + 18 = 24

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) + 18 = 24
2((-3 * -3 + x * -3) + x(-3 + x)) + 18 = 24
2((9 + -3x) + x(-3 + x)) + 18 = 24
2(9 + -3x + (-3 * x + x * x)) + 18 = 24
2(9 + -3x + (-3x + x2)) + 18 = 24

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) + 18 = 24
(9 * 2 + -6x * 2 + x2 * 2) + 18 = 24
(18 + -12x + 2x2) + 18 = 24

Reorder the terms:
18 + 18 + -12x + 2x2 = 24

Combine like terms: 18 + 18 = 36
36 + -12x + 2x2 = 24

Solving
36 + -12x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
36 + -24 + -12x + 2x2 = 24 + -24

Combine like terms: 36 + -24 = 12
12 + -12x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
12 + -12x + 2x2 = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -6x + x2 = 0

Solving
6 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -6x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -6x + x2 = 0 + -6

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

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

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -6 + 9

Reorder the terms:
9 + -6x + x2 = -6 + 9

Combine like terms: -6 + 9 = 3
9 + -6x + x2 = 3

Factor a perfect square on the left side:
(x + -3)(x + -3) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -3) equal to 1.732050808 and -1.732050808.

Subproblem 1
x + -3 = 1.732050808

Simplifying
x + -3 = 1.732050808

Reorder the terms:
-3 + x = 1.732050808

Solving
-3 + x = 1.732050808

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + x = 1.732050808 + 3
x = 1.732050808 + 3

Combine like terms: 1.732050808 + 3 = 4.732050808
x = 4.732050808

Simplifying
x = 4.732050808

Subproblem 2
x + -3 = -1.732050808

Simplifying
x + -3 = -1.732050808

Reorder the terms:
-3 + x = -1.732050808

Solving
-3 + x = -1.732050808

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + x = -1.732050808 + 3
x = -1.732050808 + 3

Combine like terms: -1.732050808 + 3 = 1.267949192
x = 1.267949192

Simplifying
x = 1.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.732050808, 1.267949192}
Solution
x = {4.732050808, 1.267949192}