2(x+3)(x-4)=2(x-3)

Solution for 2(x+3)(x-4)=2(x-3) equation:

Simplifying
2(x + 3)(x + -4) = 2(x + -3)

Reorder the terms:
2(3 + x)(x + -4) = 2(x + -3)

Reorder the terms:
2(3 + x)(-4 + x) = 2(x + -3)

Multiply (3 + x) * (-4 + x)
2(3(-4 + x) + x(-4 + x)) = 2(x + -3)
2((-4 * 3 + x * 3) + x(-4 + x)) = 2(x + -3)
2((-12 + 3x) + x(-4 + x)) = 2(x + -3)
2(-12 + 3x + (-4 * x + x * x)) = 2(x + -3)
2(-12 + 3x + (-4x + x2)) = 2(x + -3)

Combine like terms: 3x + -4x = -1x
2(-12 + -1x + x2) = 2(x + -3)
(-12 * 2 + -1x * 2 + x2 * 2) = 2(x + -3)
(-24 + -2x + 2x2) = 2(x + -3)

Reorder the terms:
-24 + -2x + 2x2 = 2(-3 + x)
-24 + -2x + 2x2 = (-3 * 2 + x * 2)
-24 + -2x + 2x2 = (-6 + 2x)

Solving
-24 + -2x + 2x2 = -6 + 2x

Solving for variable 'x'.

Reorder the terms:
-24 + 6 + -2x + -2x + 2x2 = -6 + 2x + 6 + -2x

Combine like terms: -24 + 6 = -18
-18 + -2x + -2x + 2x2 = -6 + 2x + 6 + -2x

Combine like terms: -2x + -2x = -4x
-18 + -4x + 2x2 = -6 + 2x + 6 + -2x

Reorder the terms:
-18 + -4x + 2x2 = -6 + 6 + 2x + -2x

Combine like terms: -6 + 6 = 0
-18 + -4x + 2x2 = 0 + 2x + -2x
-18 + -4x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-18 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + -2x + x2 = 0

Solving
-9 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x + x2 = 0 + 9
-2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2x + x2 = 9

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 9 + 1

Reorder the terms:
1 + -2x + x2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + -2x + x2 = 10

Factor a perfect square on the left side:
(x + -1)(x + -1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -1) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + -1 = 3.16227766

Simplifying
x + -1 = 3.16227766

Reorder the terms:
-1 + x = 3.16227766

Solving
-1 + x = 3.16227766

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.16227766 + 1
x = 3.16227766 + 1

Combine like terms: 3.16227766 + 1 = 4.16227766
x = 4.16227766

Simplifying
x = 4.16227766

Subproblem 2
x + -1 = -3.16227766

Simplifying
x + -1 = -3.16227766

Reorder the terms:
-1 + x = -3.16227766

Solving
-1 + x = -3.16227766

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.16227766 + 1
x = -3.16227766 + 1

Combine like terms: -3.16227766 + 1 = -2.16227766
x = -2.16227766

Simplifying
x = -2.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.16227766, -2.16227766}
Solution
x = {4.16227766, -2.16227766}