2(x-3)(x-3)+3=-5

Solution for 2(x-3)(x-3)+3=-5 equation:

Simplifying
2(x + -3)(x + -3) + 3 = -5

Reorder the terms:
2(-3 + x)(x + -3) + 3 = -5

Reorder the terms:
2(-3 + x)(-3 + x) + 3 = -5

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) + 3 = -5
2((-3 * -3 + x * -3) + x(-3 + x)) + 3 = -5
2((9 + -3x) + x(-3 + x)) + 3 = -5
2(9 + -3x + (-3 * x + x * x)) + 3 = -5
2(9 + -3x + (-3x + x2)) + 3 = -5

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) + 3 = -5
(9 * 2 + -6x * 2 + x2 * 2) + 3 = -5
(18 + -12x + 2x2) + 3 = -5

Reorder the terms:
18 + 3 + -12x + 2x2 = -5

Combine like terms: 18 + 3 = 21
21 + -12x + 2x2 = -5

Solving
21 + -12x + 2x2 = -5

Solving for variable 'x'.

Reorder the terms:
21 + 5 + -12x + 2x2 = -5 + 5

Combine like terms: 21 + 5 = 26
26 + -12x + 2x2 = -5 + 5

Combine like terms: -5 + 5 = 0
26 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + -6x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(13 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
13 + -6x + x2 = 0

Solving
13 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -6x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -6x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -6x + x2 = 0 + -13
-6x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-6x + x2 = -13

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 = -13 + 9

Reorder the terms:
9 + -6x + x2 = -13 + 9

Combine like terms: -13 + 9 = -4
9 + -6x + x2 = -4

Factor a perfect square on the left side:
(x + -3)(x + -3) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.