2(x+2)(x-3)+6=4(x+1)(x-6)+4

Solution for 2(x+2)(x-3)+6=4(x+1)(x-6)+4 equation:

Simplifying
2(x + 2)(x + -3) + 6 = 4(x + 1)(x + -6) + 4

Reorder the terms:
2(2 + x)(x + -3) + 6 = 4(x + 1)(x + -6) + 4

Reorder the terms:
2(2 + x)(-3 + x) + 6 = 4(x + 1)(x + -6) + 4

Multiply (2 + x) * (-3 + x)
2(2(-3 + x) + x(-3 + x)) + 6 = 4(x + 1)(x + -6) + 4
2((-3 * 2 + x * 2) + x(-3 + x)) + 6 = 4(x + 1)(x + -6) + 4
2((-6 + 2x) + x(-3 + x)) + 6 = 4(x + 1)(x + -6) + 4
2(-6 + 2x + (-3 * x + x * x)) + 6 = 4(x + 1)(x + -6) + 4
2(-6 + 2x + (-3x + x2)) + 6 = 4(x + 1)(x + -6) + 4

Combine like terms: 2x + -3x = -1x
2(-6 + -1x + x2) + 6 = 4(x + 1)(x + -6) + 4
(-6 * 2 + -1x * 2 + x2 * 2) + 6 = 4(x + 1)(x + -6) + 4
(-12 + -2x + 2x2) + 6 = 4(x + 1)(x + -6) + 4

Reorder the terms:
-12 + 6 + -2x + 2x2 = 4(x + 1)(x + -6) + 4

Combine like terms: -12 + 6 = -6
-6 + -2x + 2x2 = 4(x + 1)(x + -6) + 4

Reorder the terms:
-6 + -2x + 2x2 = 4(1 + x)(x + -6) + 4

Reorder the terms:
-6 + -2x + 2x2 = 4(1 + x)(-6 + x) + 4

Multiply (1 + x) * (-6 + x)
-6 + -2x + 2x2 = 4(1(-6 + x) + x(-6 + x)) + 4
-6 + -2x + 2x2 = 4((-6 * 1 + x * 1) + x(-6 + x)) + 4
-6 + -2x + 2x2 = 4((-6 + 1x) + x(-6 + x)) + 4
-6 + -2x + 2x2 = 4(-6 + 1x + (-6 * x + x * x)) + 4
-6 + -2x + 2x2 = 4(-6 + 1x + (-6x + x2)) + 4

Combine like terms: 1x + -6x = -5x
-6 + -2x + 2x2 = 4(-6 + -5x + x2) + 4
-6 + -2x + 2x2 = (-6 * 4 + -5x * 4 + x2 * 4) + 4
-6 + -2x + 2x2 = (-24 + -20x + 4x2) + 4

Reorder the terms:
-6 + -2x + 2x2 = -24 + 4 + -20x + 4x2

Combine like terms: -24 + 4 = -20
-6 + -2x + 2x2 = -20 + -20x + 4x2

Solving
-6 + -2x + 2x2 = -20 + -20x + 4x2

Solving for variable 'x'.

Reorder the terms:
-6 + 20 + -2x + 20x + 2x2 + -4x2 = -20 + -20x + 4x2 + 20 + 20x + -4x2

Combine like terms: -6 + 20 = 14
14 + -2x + 20x + 2x2 + -4x2 = -20 + -20x + 4x2 + 20 + 20x + -4x2

Combine like terms: -2x + 20x = 18x
14 + 18x + 2x2 + -4x2 = -20 + -20x + 4x2 + 20 + 20x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
14 + 18x + -2x2 = -20 + -20x + 4x2 + 20 + 20x + -4x2

Reorder the terms:
14 + 18x + -2x2 = -20 + 20 + -20x + 20x + 4x2 + -4x2

Combine like terms: -20 + 20 = 0
14 + 18x + -2x2 = 0 + -20x + 20x + 4x2 + -4x2
14 + 18x + -2x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
14 + 18x + -2x2 = 0 + 4x2 + -4x2
14 + 18x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
14 + 18x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 9x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 9x + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + 9x + -1x2 = 0

Solving
7 + 9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + -9x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -9x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -9x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -9x + x2 = 0 + 7
-9x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-9x + x2 = 7

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 7 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 7 + 20.25

Combine like terms: 7 + 20.25 = 27.25
20.25 + -9x + x2 = 27.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -4.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
x + -4.5 = 5.220153254

Simplifying
x + -4.5 = 5.220153254

Reorder the terms:
-4.5 + x = 5.220153254

Solving
-4.5 + x = 5.220153254

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 5.220153254 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 5.220153254 + 4.5
x = 5.220153254 + 4.5

Combine like terms: 5.220153254 + 4.5 = 9.720153254
x = 9.720153254

Simplifying
x = 9.720153254

Subproblem 2
x + -4.5 = -5.220153254

Simplifying
x + -4.5 = -5.220153254

Reorder the terms:
-4.5 + x = -5.220153254

Solving
-4.5 + x = -5.220153254

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -5.220153254 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -5.220153254 + 4.5
x = -5.220153254 + 4.5

Combine like terms: -5.220153254 + 4.5 = -0.720153254
x = -0.720153254

Simplifying
x = -0.720153254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.720153254, -0.720153254}
Solution
x = {9.720153254, -0.720153254}