(2x-6)(x+4)=936

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Solution for (2x-6)(x+4)=936 equation: 


Simplifying
(2x + -6)(x + 4) = 936

Reorder the terms:
(-6 + 2x)(x + 4) = 936

Reorder the terms:
(-6 + 2x)(4 + x) = 936

Multiply (-6 + 2x) * (4 + x)
(-6(4 + x) + 2x * (4 + x)) = 936
((4 * -6 + x * -6) + 2x * (4 + x)) = 936
((-24 + -6x) + 2x * (4 + x)) = 936
(-24 + -6x + (4 * 2x + x * 2x)) = 936
(-24 + -6x + (8x + 2x2)) = 936

Combine like terms: -6x + 8x = 2x
(-24 + 2x + 2x2) = 936

Solving
-24 + 2x + 2x2 = 936

Solving for variable 'x'.

Reorder the terms:
-24 + -936 + 2x + 2x2 = 936 + -936

Combine like terms: -24 + -936 = -960
-960 + 2x + 2x2 = 936 + -936

Combine like terms: 936 + -936 = 0
-960 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-480 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-480 + x + x2)' equal to zero and attempt to solve:

Simplifying
-480 + x + x2 = 0

Solving
-480 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '480' to each side of the equation.
-480 + x + 480 + x2 = 0 + 480

Reorder the terms:
-480 + 480 + x + x2 = 0 + 480

Combine like terms: -480 + 480 = 0
0 + x + x2 = 0 + 480
x + x2 = 0 + 480

Combine like terms: 0 + 480 = 480
x + x2 = 480

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 480 + 0.25

Reorder the terms:
0.25 + x + x2 = 480 + 0.25

Combine like terms: 480 + 0.25 = 480.25
0.25 + x + x2 = 480.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 480.25

Calculate the square root of the right side: 21.914607001

Break this problem into two subproblems by setting 
(x + 0.5) equal to 21.914607001 and -21.914607001.


Subproblem 1
x + 0.5 = 21.914607001

Simplifying
x + 0.5 = 21.914607001

Reorder the terms:
0.5 + x = 21.914607001

Solving
0.5 + x = 21.914607001

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 21.914607001 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 21.914607001 + -0.5
x = 21.914607001 + -0.5

Combine like terms: 21.914607001 + -0.5 = 21.414607001
x = 21.414607001

Simplifying
x = 21.414607001


Subproblem 2
x + 0.5 = -21.914607001

Simplifying
x + 0.5 = -21.914607001

Reorder the terms:
0.5 + x = -21.914607001

Solving
0.5 + x = -21.914607001

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -21.914607001 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -21.914607001 + -0.5
x = -21.914607001 + -0.5

Combine like terms: -21.914607001 + -0.5 = -22.414607001
x = -22.414607001

Simplifying
x = -22.414607001


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.414607001, -22.414607001}
Solution
x = {21.414607001, -22.414607001}

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