10=w(w-9)

Solution for 10=w(w-9) equation:

Simplifying
10 = w(w + -9)

Reorder the terms:
10 = w(-9 + w)
10 = (-9 * w + w * w)
10 = (-9w + w2)

Solving
10 = -9w + w2

Solving for variable 'w'.

Reorder the terms:
10 + 9w + -1w2 = -9w + 9w + w2 + -1w2

Combine like terms: -9w + 9w = 0
10 + 9w + -1w2 = 0 + w2 + -1w2
10 + 9w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
10 + 9w + -1w2 = 0

Factor a trinomial.
(10 + -1w)(1 + w) = 0

Subproblem 1
Set the factor '(10 + -1w)' equal to zero and attempt to solve:

Simplifying
10 + -1w = 0

Solving
10 + -1w = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1w = 0 + -10
-1w = 0 + -10

Combine like terms: 0 + -10 = -10
-1w = -10

Divide each side by '-1'.
w = 10

Simplifying
w = 10
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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 = 0 + -1

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

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

Simplifying
w = -1
Solution
w = {10, -1}