(w-3)*2(w+7)=114

Solution for (w-3)*2(w+7)=114 equation:

Simplifying
(w + -3) * 2(w + 7) = 114

Reorder the terms:
(-3 + w) * 2(w + 7) = 114

Reorder the terms:
(-3 + w) * 2(7 + w) = 114

Reorder the terms for easier multiplication:
2(-3 + w)(7 + w) = 114

Multiply (-3 + w) * (7 + w)
2(-3(7 + w) + w(7 + w)) = 114
2((7 * -3 + w * -3) + w(7 + w)) = 114
2((-21 + -3w) + w(7 + w)) = 114
2(-21 + -3w + (7 * w + w * w)) = 114
2(-21 + -3w + (7w + w2)) = 114

Combine like terms: -3w + 7w = 4w
2(-21 + 4w + w2) = 114
(-21 * 2 + 4w * 2 + w2 * 2) = 114
(-42 + 8w + 2w2) = 114

Solving
-42 + 8w + 2w2 = 114

Solving for variable 'w'.

Reorder the terms:
-42 + -114 + 8w + 2w2 = 114 + -114

Combine like terms: -42 + -114 = -156
-156 + 8w + 2w2 = 114 + -114

Combine like terms: 114 + -114 = 0
-156 + 8w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-78 + 4w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-78 + 4w + w2)' equal to zero and attempt to solve:

Simplifying
-78 + 4w + w2 = 0

Solving
-78 + 4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + 4w + 78 + w2 = 0 + 78

Reorder the terms:
-78 + 78 + 4w + w2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + 4w + w2 = 0 + 78
4w + w2 = 0 + 78

Combine like terms: 0 + 78 = 78
4w + w2 = 78

The w term is 4w.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4w + 4 + w2 = 78 + 4

Reorder the terms:
4 + 4w + w2 = 78 + 4

Combine like terms: 78 + 4 = 82
4 + 4w + w2 = 82

Factor a perfect square on the left side:
(w + 2)(w + 2) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(w + 2) equal to 9.055385138 and -9.055385138.

Subproblem 1
w + 2 = 9.055385138

Simplifying
w + 2 = 9.055385138

Reorder the terms:
2 + w = 9.055385138

Solving
2 + w = 9.055385138

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = 9.055385138 + -2

Combine like terms: 2 + -2 = 0
0 + w = 9.055385138 + -2
w = 9.055385138 + -2

Combine like terms: 9.055385138 + -2 = 7.055385138
w = 7.055385138

Simplifying
w = 7.055385138

Subproblem 2
w + 2 = -9.055385138

Simplifying
w + 2 = -9.055385138

Reorder the terms:
2 + w = -9.055385138

Solving
2 + w = -9.055385138

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = -9.055385138 + -2

Combine like terms: 2 + -2 = 0
0 + w = -9.055385138 + -2
w = -9.055385138 + -2

Combine like terms: -9.055385138 + -2 = -11.055385138
w = -11.055385138

Simplifying
w = -11.055385138

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.055385138, -11.055385138}
Solution
w = {7.055385138, -11.055385138}