(x-2)(2x+10)-112=0

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Solution for (x-2)(2x+10)-112=0 equation: 


Simplifying
(x + -2)(2x + 10) + -112 = 0

Reorder the terms:
(-2 + x)(2x + 10) + -112 = 0

Reorder the terms:
(-2 + x)(10 + 2x) + -112 = 0

Multiply (-2 + x) * (10 + 2x)
(-2(10 + 2x) + x(10 + 2x)) + -112 = 0
((10 * -2 + 2x * -2) + x(10 + 2x)) + -112 = 0
((-20 + -4x) + x(10 + 2x)) + -112 = 0
(-20 + -4x + (10 * x + 2x * x)) + -112 = 0
(-20 + -4x + (10x + 2x2)) + -112 = 0

Combine like terms: -4x + 10x = 6x
(-20 + 6x + 2x2) + -112 = 0

Reorder the terms:
-20 + -112 + 6x + 2x2 = 0

Combine like terms: -20 + -112 = -132
-132 + 6x + 2x2 = 0

Solving
-132 + 6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-66 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-66 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-66 + 3x + x2 = 0

Solving
-66 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 3x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + 3x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 3x + x2 = 0 + 66
3x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
3x + x2 = 66

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 66 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 66 + 2.25

Combine like terms: 66 + 2.25 = 68.25
2.25 + 3x + x2 = 68.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(x + 1.5) equal to 8.261355821 and -8.261355821.


Subproblem 1
x + 1.5 = 8.261355821

Simplifying
x + 1.5 = 8.261355821

Reorder the terms:
1.5 + x = 8.261355821

Solving
1.5 + x = 8.261355821

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 8.261355821 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 8.261355821 + -1.5
x = 8.261355821 + -1.5

Combine like terms: 8.261355821 + -1.5 = 6.761355821
x = 6.761355821

Simplifying
x = 6.761355821


Subproblem 2
x + 1.5 = -8.261355821

Simplifying
x + 1.5 = -8.261355821

Reorder the terms:
1.5 + x = -8.261355821

Solving
1.5 + x = -8.261355821

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -8.261355821 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -8.261355821 + -1.5
x = -8.261355821 + -1.5

Combine like terms: -8.261355821 + -1.5 = -9.761355821
x = -9.761355821

Simplifying
x = -9.761355821


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.761355821, -9.761355821}
Solution
x = {6.761355821, -9.761355821}

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