4=9-3(2w+1)5w

Solution for 4=9-3(2w+1)5w equation:

Simplifying
4 = 9 + -3(2w + 1) * 5w

Reorder the terms:
4 = 9 + -3(1 + 2w) * 5w

Reorder the terms for easier multiplication:
4 = 9 + -3 * 5w(1 + 2w)

Multiply -3 * 5
4 = 9 + -15w(1 + 2w)
4 = 9 + (1 * -15w + 2w * -15w)
4 = 9 + (-15w + -30w2)

Solving
4 = 9 + -15w + -30w2

Solving for variable 'w'.

Combine like terms: 4 + -9 = -5
-5 + 15w + 30w2 = 9 + -15w + -30w2 + -9 + 15w + 30w2

Reorder the terms:
-5 + 15w + 30w2 = 9 + -9 + -15w + 15w + -30w2 + 30w2

Combine like terms: 9 + -9 = 0
-5 + 15w + 30w2 = 0 + -15w + 15w + -30w2 + 30w2
-5 + 15w + 30w2 = -15w + 15w + -30w2 + 30w2

Combine like terms: -15w + 15w = 0
-5 + 15w + 30w2 = 0 + -30w2 + 30w2
-5 + 15w + 30w2 = -30w2 + 30w2

Combine like terms: -30w2 + 30w2 = 0
-5 + 15w + 30w2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 3w + 6w2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + 3w + 6w2)' equal to zero and attempt to solve:

Simplifying
-1 + 3w + 6w2 = 0

Solving
-1 + 3w + 6w2 = 0

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

Divide each side by '6'.
-0.1666666667 + 0.5w + w2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.5w + 0.1666666667 + w2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 0.5w + w2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 0.5w + w2 = 0 + 0.1666666667
0.5w + w2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
0.5w + w2 = 0.1666666667

The w term is 0.5w.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5w + 0.0625 + w2 = 0.1666666667 + 0.0625

Reorder the terms:
0.0625 + 0.5w + w2 = 0.1666666667 + 0.0625

Combine like terms: 0.1666666667 + 0.0625 = 0.2291666667
0.0625 + 0.5w + w2 = 0.2291666667

Factor a perfect square on the left side:
(w + 0.25)(w + 0.25) = 0.2291666667

Calculate the square root of the right side: 0.478713554

Break this problem into two subproblems by setting 
(w + 0.25) equal to 0.478713554 and -0.478713554.

Subproblem 1
w + 0.25 = 0.478713554

Simplifying
w + 0.25 = 0.478713554

Reorder the terms:
0.25 + w = 0.478713554

Solving
0.25 + w = 0.478713554

Solving for variable 'w'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + w = 0.478713554 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + w = 0.478713554 + -0.25
w = 0.478713554 + -0.25

Combine like terms: 0.478713554 + -0.25 = 0.228713554
w = 0.228713554

Simplifying
w = 0.228713554

Subproblem 2
w + 0.25 = -0.478713554

Simplifying
w + 0.25 = -0.478713554

Reorder the terms:
0.25 + w = -0.478713554

Solving
0.25 + w = -0.478713554

Solving for variable 'w'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + w = -0.478713554 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + w = -0.478713554 + -0.25
w = -0.478713554 + -0.25

Combine like terms: -0.478713554 + -0.25 = -0.728713554
w = -0.728713554

Simplifying
w = -0.728713554

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.228713554, -0.728713554}
Solution
w = {0.228713554, -0.728713554}