10w^2+12w-168=0

Solution for 10w^2+12w-168=0 equation:

Simplifying
10w2 + 12w + -168 = 0

Reorder the terms:
-168 + 12w + 10w2 = 0

Solving
-168 + 12w + 10w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-84 + 6w + 5w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-84 + 6w + 5w2)' equal to zero and attempt to solve:

Simplifying
-84 + 6w + 5w2 = 0

Solving
-84 + 6w + 5w2 = 0

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

Divide each side by '5'.
-16.8 + 1.2w + w2 = 0

Move the constant term to the right:

Add '16.8' to each side of the equation.
-16.8 + 1.2w + 16.8 + w2 = 0 + 16.8

Reorder the terms:
-16.8 + 16.8 + 1.2w + w2 = 0 + 16.8

Combine like terms: -16.8 + 16.8 = 0.0
0.0 + 1.2w + w2 = 0 + 16.8
1.2w + w2 = 0 + 16.8

Combine like terms: 0 + 16.8 = 16.8
1.2w + w2 = 16.8

The w term is 1.2w.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2w + 0.36 + w2 = 16.8 + 0.36

Reorder the terms:
0.36 + 1.2w + w2 = 16.8 + 0.36

Combine like terms: 16.8 + 0.36 = 17.16
0.36 + 1.2w + w2 = 17.16

Factor a perfect square on the left side:
(w + 0.6)(w + 0.6) = 17.16

Calculate the square root of the right side: 4.142463035

Break this problem into two subproblems by setting 
(w + 0.6) equal to 4.142463035 and -4.142463035.

Subproblem 1
w + 0.6 = 4.142463035

Simplifying
w + 0.6 = 4.142463035

Reorder the terms:
0.6 + w = 4.142463035

Solving
0.6 + w = 4.142463035

Solving for variable 'w'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + w = 4.142463035 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + w = 4.142463035 + -0.6
w = 4.142463035 + -0.6

Combine like terms: 4.142463035 + -0.6 = 3.542463035
w = 3.542463035

Simplifying
w = 3.542463035

Subproblem 2
w + 0.6 = -4.142463035

Simplifying
w + 0.6 = -4.142463035

Reorder the terms:
0.6 + w = -4.142463035

Solving
0.6 + w = -4.142463035

Solving for variable 'w'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + w = -4.142463035 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + w = -4.142463035 + -0.6
w = -4.142463035 + -0.6

Combine like terms: -4.142463035 + -0.6 = -4.742463035
w = -4.742463035

Simplifying
w = -4.742463035

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.542463035, -4.742463035}
Solution
w = {3.542463035, -4.742463035}