150=2(3+w)*(w-1)

Solution for 150=2(3+w)*(w-1) equation:

Simplifying
150 = 2(3 + w)(w + -1)

Reorder the terms:
150 = 2(3 + w)(-1 + w)

Multiply (3 + w) * (-1 + w)
150 = 2(3(-1 + w) + w(-1 + w))
150 = 2((-1 * 3 + w * 3) + w(-1 + w))
150 = 2((-3 + 3w) + w(-1 + w))
150 = 2(-3 + 3w + (-1 * w + w * w))
150 = 2(-3 + 3w + (-1w + w2))

Combine like terms: 3w + -1w = 2w
150 = 2(-3 + 2w + w2)
150 = (-3 * 2 + 2w * 2 + w2 * 2)
150 = (-6 + 4w + 2w2)

Solving
150 = -6 + 4w + 2w2

Solving for variable 'w'.

Combine like terms: 150 + 6 = 156
156 + -4w + -2w2 = -6 + 4w + 2w2 + 6 + -4w + -2w2

Reorder the terms:
156 + -4w + -2w2 = -6 + 6 + 4w + -4w + 2w2 + -2w2

Combine like terms: -6 + 6 = 0
156 + -4w + -2w2 = 0 + 4w + -4w + 2w2 + -2w2
156 + -4w + -2w2 = 4w + -4w + 2w2 + -2w2

Combine like terms: 4w + -4w = 0
156 + -4w + -2w2 = 0 + 2w2 + -2w2
156 + -4w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
156 + -4w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(78 + -2w + -1w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(78 + -2w + -1w2)' equal to zero and attempt to solve:

Simplifying
78 + -2w + -1w2 = 0

Solving
78 + -2w + -1w2 = 0

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

Divide each side by '-1'.
-78 + 2w + w2 = 0

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + 2w + 78 + w2 = 0 + 78

Reorder the terms:
-78 + 78 + 2w + w2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + 2w + w2 = 0 + 78
2w + w2 = 0 + 78

Combine like terms: 0 + 78 = 78
2w + w2 = 78

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 78 + 1

Reorder the terms:
1 + 2w + w2 = 78 + 1

Combine like terms: 78 + 1 = 79
1 + 2w + w2 = 79

Factor a perfect square on the left side:
(w + 1)(w + 1) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(w + 1) equal to 8.888194417 and -8.888194417.

Subproblem 1
w + 1 = 8.888194417

Simplifying
w + 1 = 8.888194417

Reorder the terms:
1 + w = 8.888194417

Solving
1 + w = 8.888194417

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = 8.888194417 + -1

Combine like terms: 1 + -1 = 0
0 + w = 8.888194417 + -1
w = 8.888194417 + -1

Combine like terms: 8.888194417 + -1 = 7.888194417
w = 7.888194417

Simplifying
w = 7.888194417

Subproblem 2
w + 1 = -8.888194417

Simplifying
w + 1 = -8.888194417

Reorder the terms:
1 + w = -8.888194417

Solving
1 + w = -8.888194417

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = -8.888194417 + -1

Combine like terms: 1 + -1 = 0
0 + w = -8.888194417 + -1
w = -8.888194417 + -1

Combine like terms: -8.888194417 + -1 = -9.888194417
w = -9.888194417

Simplifying
w = -9.888194417

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.888194417, -9.888194417}
Solution
w = {7.888194417, -9.888194417}