42=w(w-11)

Solution for 42=w(w-11) equation:

Simplifying
42 = w(w + -11)

Reorder the terms:
42 = w(-11 + w)
42 = (-11 * w + w * w)
42 = (-11w + w2)

Solving
42 = -11w + w2

Solving for variable 'w'.

Reorder the terms:
42 + 11w + -1w2 = -11w + 11w + w2 + -1w2

Combine like terms: -11w + 11w = 0
42 + 11w + -1w2 = 0 + w2 + -1w2
42 + 11w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
42 + 11w + -1w2 = 0

Factor a trinomial.
(14 + -1w)(3 + w) = 0

Subproblem 1
Set the factor '(14 + -1w)' equal to zero and attempt to solve:

Simplifying
14 + -1w = 0

Solving
14 + -1w = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1w = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1w = 0 + -14
-1w = 0 + -14

Combine like terms: 0 + -14 = -14
-1w = -14

Divide each side by '-1'.
w = 14

Simplifying
w = 14
Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 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 + w = 0 + -3

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

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

Simplifying
w = -3
Solution
w = {14, -3}