91=(w+6)(w)

Solution for 91=(w+6)(w) equation:

Simplifying
91 = (w + 6)(w)

Reorder the terms:
91 = (6 + w)(w)

Reorder the terms for easier multiplication:
91 = w(6 + w)
91 = (6 * w + w * w)
91 = (6w + w2)

Solving
91 = 6w + w2

Solving for variable 'w'.

Reorder the terms:
91 + -6w + -1w2 = 6w + -6w + w2 + -1w2

Combine like terms: 6w + -6w = 0
91 + -6w + -1w2 = 0 + w2 + -1w2
91 + -6w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
91 + -6w + -1w2 = 0

Factor a trinomial.
(7 + -1w)(13 + w) = 0

Subproblem 1
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Subproblem 2
Set the factor '(13 + w)' equal to zero and attempt to solve:

Simplifying
13 + w = 0

Solving
13 + w = 0

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

Add '-13' to each side of the equation.
13 + -13 + w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + w = 0 + -13
w = 0 + -13

Combine like terms: 0 + -13 = -13
w = -13

Simplifying
w = -13
Solution
w = {7, -13}