-2w(w-7)+10w=34

Solution for -2w(w-7)+10w=34 equation:

Simplifying
-2w(w + -7) + 10w = 34

Reorder the terms:
-2w(-7 + w) + 10w = 34
(-7 * -2w + w * -2w) + 10w = 34
(14w + -2w2) + 10w = 34

Reorder the terms:
14w + 10w + -2w2 = 34

Combine like terms: 14w + 10w = 24w
24w + -2w2 = 34

Solving
24w + -2w2 = 34

Solving for variable 'w'.

Reorder the terms:
-34 + 24w + -2w2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 24w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 12w + -1w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + 12w + -1w2)' equal to zero and attempt to solve:

Simplifying
-17 + 12w + -1w2 = 0

Solving
-17 + 12w + -1w2 = 0

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

Divide each side by '-1'.
17 + -12w + w2 = 0

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -12w + -17 + w2 = 0 + -17

Reorder the terms:
17 + -17 + -12w + w2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -12w + w2 = 0 + -17
-12w + w2 = 0 + -17

Combine like terms: 0 + -17 = -17
-12w + w2 = -17

The w term is -12w.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12w + 36 + w2 = -17 + 36

Reorder the terms:
36 + -12w + w2 = -17 + 36

Combine like terms: -17 + 36 = 19
36 + -12w + w2 = 19

Factor a perfect square on the left side:
(w + -6)(w + -6) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(w + -6) equal to 4.358898944 and -4.358898944.

Subproblem 1
w + -6 = 4.358898944

Simplifying
w + -6 = 4.358898944

Reorder the terms:
-6 + w = 4.358898944

Solving
-6 + w = 4.358898944

Solving for variable 'w'.

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

Add '6' to each side of the equation.
-6 + 6 + w = 4.358898944 + 6

Combine like terms: -6 + 6 = 0
0 + w = 4.358898944 + 6
w = 4.358898944 + 6

Combine like terms: 4.358898944 + 6 = 10.358898944
w = 10.358898944

Simplifying
w = 10.358898944

Subproblem 2
w + -6 = -4.358898944

Simplifying
w + -6 = -4.358898944

Reorder the terms:
-6 + w = -4.358898944

Solving
-6 + w = -4.358898944

Solving for variable 'w'.

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

Add '6' to each side of the equation.
-6 + 6 + w = -4.358898944 + 6

Combine like terms: -6 + 6 = 0
0 + w = -4.358898944 + 6
w = -4.358898944 + 6

Combine like terms: -4.358898944 + 6 = 1.641101056
w = 1.641101056

Simplifying
w = 1.641101056

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.358898944, 1.641101056}
Solution
w = {10.358898944, 1.641101056}