15=(4w-7)(w)

Solution for 15=(4w-7)(w) equation:

Simplifying
15 = (4w + -7)(w)

Reorder the terms:
15 = (-7 + 4w)(w)

Reorder the terms for easier multiplication:
15 = w(-7 + 4w)
15 = (-7 * w + 4w * w)
15 = (-7w + 4w2)

Solving
15 = -7w + 4w2

Solving for variable 'w'.

Reorder the terms:
15 + 7w + -4w2 = -7w + 7w + 4w2 + -4w2

Combine like terms: -7w + 7w = 0
15 + 7w + -4w2 = 0 + 4w2 + -4w2
15 + 7w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
15 + 7w + -4w2 = 0

Factor a trinomial.
(3 + -1w)(5 + 4w) = 0

Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Subproblem 2
Set the factor '(5 + 4w)' equal to zero and attempt to solve:

Simplifying
5 + 4w = 0

Solving
5 + 4w = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4w = 0 + -5
4w = 0 + -5

Combine like terms: 0 + -5 = -5
4w = -5

Divide each side by '4'.
w = -1.25

Simplifying
w = -1.25
Solution
w = {3, -1.25}