112=2(x+5)(x-2)

Solution for 112=2(x+5)(x-2) equation:

Simplifying
112 = 2(x + 5)(x + -2)

Reorder the terms:
112 = 2(5 + x)(x + -2)

Reorder the terms:
112 = 2(5 + x)(-2 + x)

Multiply (5 + x) * (-2 + x)
112 = 2(5(-2 + x) + x(-2 + x))
112 = 2((-2 * 5 + x * 5) + x(-2 + x))
112 = 2((-10 + 5x) + x(-2 + x))
112 = 2(-10 + 5x + (-2 * x + x * x))
112 = 2(-10 + 5x + (-2x + x2))

Combine like terms: 5x + -2x = 3x
112 = 2(-10 + 3x + x2)
112 = (-10 * 2 + 3x * 2 + x2 * 2)
112 = (-20 + 6x + 2x2)

Solving
112 = -20 + 6x + 2x2

Solving for variable 'x'.

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

Reorder the terms:
132 + -6x + -2x2 = -20 + 20 + 6x + -6x + 2x2 + -2x2

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(66 + -3x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(66 + -3x + -1x2)' equal to zero and attempt to solve:

Simplifying
66 + -3x + -1x2 = 0

Solving
66 + -3x + -1x2 = 0

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

Divide each side by '-1'.
-66 + 3x + x2 = 0

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}