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

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

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

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

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

Multiply (5 + w) * (-2 + w)
2(5(-2 + w) + w(-2 + w)) = 112
2((-2 * 5 + w * 5) + w(-2 + w)) = 112
2((-10 + 5w) + w(-2 + w)) = 112
2(-10 + 5w + (-2 * w + w * w)) = 112
2(-10 + 5w + (-2w + w2)) = 112

Combine like terms: 5w + -2w = 3w
2(-10 + 3w + w2) = 112
(-10 * 2 + 3w * 2 + w2 * 2) = 112
(-20 + 6w + 2w2) = 112

Solving
-20 + 6w + 2w2 = 112

Solving for variable 'w'.

Reorder the terms:
-20 + -112 + 6w + 2w2 = 112 + -112

Combine like terms: -20 + -112 = -132
-132 + 6w + 2w2 = 112 + -112

Combine like terms: 112 + -112 = 0
-132 + 6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-66 + 3w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-66 + 3w + w2)' equal to zero and attempt to solve:

Simplifying
-66 + 3w + w2 = 0

Solving
-66 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 3w + 66 + w2 = 0 + 66

Reorder the terms:
-66 + 66 + 3w + w2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 3w + w2 = 0 + 66
3w + w2 = 0 + 66

Combine like terms: 0 + 66 = 66
3w + w2 = 66

The w term is 3w.  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.
3w + 2.25 + w2 = 66 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 66 + 2.25

Combine like terms: 66 + 2.25 = 68.25
2.25 + 3w + w2 = 68.25

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

Calculate the square root of the right side: 8.261355821

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

Subproblem 1
w + 1.5 = 8.261355821

Simplifying
w + 1.5 = 8.261355821

Reorder the terms:
1.5 + w = 8.261355821

Solving
1.5 + w = 8.261355821

Solving for variable 'w'.

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

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

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

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

Simplifying
w = 6.761355821

Subproblem 2
w + 1.5 = -8.261355821

Simplifying
w + 1.5 = -8.261355821

Reorder the terms:
1.5 + w = -8.261355821

Solving
1.5 + w = -8.261355821

Solving for variable 'w'.

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

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

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

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

Simplifying
w = -9.761355821

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