-5(w+1)=5w(4w+6)

Solution for -5(w+1)=5w(4w+6) equation:

Simplifying
-5(w + 1) = 5w(4w + 6)

Reorder the terms:
-5(1 + w) = 5w(4w + 6)
(1 * -5 + w * -5) = 5w(4w + 6)
(-5 + -5w) = 5w(4w + 6)

Reorder the terms:
-5 + -5w = 5w(6 + 4w)
-5 + -5w = (6 * 5w + 4w * 5w)
-5 + -5w = (30w + 20w2)

Solving
-5 + -5w = 30w + 20w2

Solving for variable 'w'.

Combine like terms: -5w + -30w = -35w
-5 + -35w + -20w2 = 30w + 20w2 + -30w + -20w2

Reorder the terms:
-5 + -35w + -20w2 = 30w + -30w + 20w2 + -20w2

Combine like terms: 30w + -30w = 0
-5 + -35w + -20w2 = 0 + 20w2 + -20w2
-5 + -35w + -20w2 = 20w2 + -20w2

Combine like terms: 20w2 + -20w2 = 0
-5 + -35w + -20w2 = 0

Factor out the Greatest Common Factor (GCF), '-5'.
-5(1 + 7w + 4w2) = 0

Ignore the factor -5.
Subproblem 1
Set the factor '(1 + 7w + 4w2)' equal to zero and attempt to solve:

Simplifying
1 + 7w + 4w2 = 0

Solving
1 + 7w + 4w2 = 0

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

Divide each side by '4'.
0.25 + 1.75w + w2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 1.75w + -0.25 + w2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 1.75w + w2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 1.75w + w2 = 0 + -0.25
1.75w + w2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
1.75w + w2 = -0.25

The w term is 1.75w.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75w + 0.765625 + w2 = -0.25 + 0.765625

Reorder the terms:
0.765625 + 1.75w + w2 = -0.25 + 0.765625

Combine like terms: -0.25 + 0.765625 = 0.515625
0.765625 + 1.75w + w2 = 0.515625

Factor a perfect square on the left side:
(w + 0.875)(w + 0.875) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(w + 0.875) equal to 0.718070331 and -0.718070331.

Subproblem 1
w + 0.875 = 0.718070331

Simplifying
w + 0.875 = 0.718070331

Reorder the terms:
0.875 + w = 0.718070331

Solving
0.875 + w = 0.718070331

Solving for variable 'w'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + w = 0.718070331 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + w = 0.718070331 + -0.875
w = 0.718070331 + -0.875

Combine like terms: 0.718070331 + -0.875 = -0.156929669
w = -0.156929669

Simplifying
w = -0.156929669

Subproblem 2
w + 0.875 = -0.718070331

Simplifying
w + 0.875 = -0.718070331

Reorder the terms:
0.875 + w = -0.718070331

Solving
0.875 + w = -0.718070331

Solving for variable 'w'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + w = -0.718070331 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + w = -0.718070331 + -0.875
w = -0.718070331 + -0.875

Combine like terms: -0.718070331 + -0.875 = -1.593070331
w = -1.593070331

Simplifying
w = -1.593070331

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.156929669, -1.593070331}
Solution
w = {-0.156929669, -1.593070331}