12w^2+8w=-7w^2-3w+14

Solution for 12w^2+8w=-7w^2-3w+14 equation:

Simplifying
12w2 + 8w = -7w2 + -3w + 14

Reorder the terms:
8w + 12w2 = -7w2 + -3w + 14

Reorder the terms:
8w + 12w2 = 14 + -3w + -7w2

Solving
8w + 12w2 = 14 + -3w + -7w2

Solving for variable 'w'.

Reorder the terms:
-14 + 8w + 3w + 12w2 + 7w2 = 14 + -3w + -7w2 + -14 + 3w + 7w2

Combine like terms: 8w + 3w = 11w
-14 + 11w + 12w2 + 7w2 = 14 + -3w + -7w2 + -14 + 3w + 7w2

Combine like terms: 12w2 + 7w2 = 19w2
-14 + 11w + 19w2 = 14 + -3w + -7w2 + -14 + 3w + 7w2

Reorder the terms:
-14 + 11w + 19w2 = 14 + -14 + -3w + 3w + -7w2 + 7w2

Combine like terms: 14 + -14 = 0
-14 + 11w + 19w2 = 0 + -3w + 3w + -7w2 + 7w2
-14 + 11w + 19w2 = -3w + 3w + -7w2 + 7w2

Combine like terms: -3w + 3w = 0
-14 + 11w + 19w2 = 0 + -7w2 + 7w2
-14 + 11w + 19w2 = -7w2 + 7w2

Combine like terms: -7w2 + 7w2 = 0
-14 + 11w + 19w2 = 0

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

Divide each side by '19'.
-0.7368421053 + 0.5789473684w + w2 = 0

Move the constant term to the right:

Add '0.7368421053' to each side of the equation.
-0.7368421053 + 0.5789473684w + 0.7368421053 + w2 = 0 + 0.7368421053

Reorder the terms:
-0.7368421053 + 0.7368421053 + 0.5789473684w + w2 = 0 + 0.7368421053

Combine like terms: -0.7368421053 + 0.7368421053 = 0.0000000000
0.0000000000 + 0.5789473684w + w2 = 0 + 0.7368421053
0.5789473684w + w2 = 0 + 0.7368421053

Combine like terms: 0 + 0.7368421053 = 0.7368421053
0.5789473684w + w2 = 0.7368421053

The w term is 0.5789473684w.  Take half its coefficient (0.2894736842).
Square it (0.08379501384) and add it to both sides.

Add '0.08379501384' to each side of the equation.
0.5789473684w + 0.08379501384 + w2 = 0.7368421053 + 0.08379501384

Reorder the terms:
0.08379501384 + 0.5789473684w + w2 = 0.7368421053 + 0.08379501384

Combine like terms: 0.7368421053 + 0.08379501384 = 0.82063711914
0.08379501384 + 0.5789473684w + w2 = 0.82063711914

Factor a perfect square on the left side:
(w + 0.2894736842)(w + 0.2894736842) = 0.82063711914

Calculate the square root of the right side: 0.905890236

Break this problem into two subproblems by setting 
(w + 0.2894736842) equal to 0.905890236 and -0.905890236.

Subproblem 1
w + 0.2894736842 = 0.905890236

Simplifying
w + 0.2894736842 = 0.905890236

Reorder the terms:
0.2894736842 + w = 0.905890236

Solving
0.2894736842 + w = 0.905890236

Solving for variable 'w'.

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

Add '-0.2894736842' to each side of the equation.
0.2894736842 + -0.2894736842 + w = 0.905890236 + -0.2894736842

Combine like terms: 0.2894736842 + -0.2894736842 = 0.0000000000
0.0000000000 + w = 0.905890236 + -0.2894736842
w = 0.905890236 + -0.2894736842

Combine like terms: 0.905890236 + -0.2894736842 = 0.6164165518
w = 0.6164165518

Simplifying
w = 0.6164165518

Subproblem 2
w + 0.2894736842 = -0.905890236

Simplifying
w + 0.2894736842 = -0.905890236

Reorder the terms:
0.2894736842 + w = -0.905890236

Solving
0.2894736842 + w = -0.905890236

Solving for variable 'w'.

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

Add '-0.2894736842' to each side of the equation.
0.2894736842 + -0.2894736842 + w = -0.905890236 + -0.2894736842

Combine like terms: 0.2894736842 + -0.2894736842 = 0.0000000000
0.0000000000 + w = -0.905890236 + -0.2894736842
w = -0.905890236 + -0.2894736842

Combine like terms: -0.905890236 + -0.2894736842 = -1.1953639202
w = -1.1953639202

Simplifying
w = -1.1953639202

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.6164165518, -1.1953639202}