-3w(w+5)+5w=2(w-6)

Solution for -3w(w+5)+5w=2(w-6) equation:

Simplifying
-3w(w + 5) + 5w = 2(w + -6)

Reorder the terms:
-3w(5 + w) + 5w = 2(w + -6)
(5 * -3w + w * -3w) + 5w = 2(w + -6)
(-15w + -3w2) + 5w = 2(w + -6)

Reorder the terms:
-15w + 5w + -3w2 = 2(w + -6)

Combine like terms: -15w + 5w = -10w
-10w + -3w2 = 2(w + -6)

Reorder the terms:
-10w + -3w2 = 2(-6 + w)
-10w + -3w2 = (-6 * 2 + w * 2)
-10w + -3w2 = (-12 + 2w)

Solving
-10w + -3w2 = -12 + 2w

Solving for variable 'w'.

Reorder the terms:
12 + -10w + -2w + -3w2 = -12 + 2w + 12 + -2w

Combine like terms: -10w + -2w = -12w
12 + -12w + -3w2 = -12 + 2w + 12 + -2w

Reorder the terms:
12 + -12w + -3w2 = -12 + 12 + 2w + -2w

Combine like terms: -12 + 12 = 0
12 + -12w + -3w2 = 0 + 2w + -2w
12 + -12w + -3w2 = 2w + -2w

Combine like terms: 2w + -2w = 0
12 + -12w + -3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -4w + -1w2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -4w + -1w2)' equal to zero and attempt to solve:

Simplifying
4 + -4w + -1w2 = 0

Solving
4 + -4w + -1w2 = 0

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

Divide each side by '-1'.
-4 + 4w + w2 = 0

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + 4w + w2 = 8

Factor a perfect square on the left side:
(w + 2)(w + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(w + 2) equal to 2.828427125 and -2.828427125.

Subproblem 1
w + 2 = 2.828427125

Simplifying
w + 2 = 2.828427125

Reorder the terms:
2 + w = 2.828427125

Solving
2 + w = 2.828427125

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 = 2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + w = 2.828427125 + -2
w = 2.828427125 + -2

Combine like terms: 2.828427125 + -2 = 0.828427125
w = 0.828427125

Simplifying
w = 0.828427125

Subproblem 2
w + 2 = -2.828427125

Simplifying
w + 2 = -2.828427125

Reorder the terms:
2 + w = -2.828427125

Solving
2 + w = -2.828427125

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 = -2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + w = -2.828427125 + -2
w = -2.828427125 + -2

Combine like terms: -2.828427125 + -2 = -4.828427125
w = -4.828427125

Simplifying
w = -4.828427125

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.828427125, -4.828427125}
Solution
w = {0.828427125, -4.828427125}