150=w(4w-1)

Solution for 150=w(4w-1) equation:

Simplifying
150 = w(4w + -1)

Reorder the terms:
150 = w(-1 + 4w)
150 = (-1 * w + 4w * w)
150 = (-1w + 4w2)

Solving
150 = -1w + 4w2

Solving for variable 'w'.

Reorder the terms:
150 + w + -4w2 = -1w + w + 4w2 + -4w2

Combine like terms: -1w + w = 0
150 + w + -4w2 = 0 + 4w2 + -4w2
150 + w + -4w2 = 4w2 + -4w2

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

Factor a trinomial.
(25 + -4w)(6 + w) = 0

Subproblem 1
Set the factor '(25 + -4w)' equal to zero and attempt to solve:

Simplifying
25 + -4w = 0

Solving
25 + -4w = 0

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

Add '-25' to each side of the equation.
25 + -25 + -4w = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -4w = 0 + -25
-4w = 0 + -25

Combine like terms: 0 + -25 = -25
-4w = -25

Divide each side by '-4'.
w = 6.25

Simplifying
w = 6.25
Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Solution
w = {6.25, -6}