3w(5w^2+2w-8)=

Solution for 3w(5w^2+2w-8)= equation:

Simplifying
3w(5w2 + 2w + -8) = 0

Reorder the terms:
3w(-8 + 2w + 5w2) = 0
(-8 * 3w + 2w * 3w + 5w2 * 3w) = 0
(-24w + 6w2 + 15w3) = 0

Solving
-24w + 6w2 + 15w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w'.
3w(-8 + 2w + 5w2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
Set the factor '(-8 + 2w + 5w2)' equal to zero and attempt to solve:

Simplifying
-8 + 2w + 5w2 = 0

Solving
-8 + 2w + 5w2 = 0

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

Divide each side by '5'.
-1.6 + 0.4w + w2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.4w + 1.6 + w2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.4w + w2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.4w + w2 = 0 + 1.6
0.4w + w2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
0.4w + w2 = 1.6

The w term is 0.4w.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4w + 0.04 + w2 = 1.6 + 0.04

Reorder the terms:
0.04 + 0.4w + w2 = 1.6 + 0.04

Combine like terms: 1.6 + 0.04 = 1.64
0.04 + 0.4w + w2 = 1.64

Factor a perfect square on the left side:
(w + 0.2)(w + 0.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(w + 0.2) equal to 1.280624847 and -1.280624847.

Subproblem 1
w + 0.2 = 1.280624847

Simplifying
w + 0.2 = 1.280624847

Reorder the terms:
0.2 + w = 1.280624847

Solving
0.2 + w = 1.280624847

Solving for variable 'w'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + w = 1.280624847 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + w = 1.280624847 + -0.2
w = 1.280624847 + -0.2

Combine like terms: 1.280624847 + -0.2 = 1.080624847
w = 1.080624847

Simplifying
w = 1.080624847

Subproblem 2
w + 0.2 = -1.280624847

Simplifying
w + 0.2 = -1.280624847

Reorder the terms:
0.2 + w = -1.280624847

Solving
0.2 + w = -1.280624847

Solving for variable 'w'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + w = -1.280624847 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + w = -1.280624847 + -0.2
w = -1.280624847 + -0.2

Combine like terms: -1.280624847 + -0.2 = -1.480624847
w = -1.480624847

Simplifying
w = -1.480624847

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.080624847, -1.480624847}
Solution
w = {0, 1.080624847, -1.480624847}