w^2-22w=23

Solution for w^2-22w=23 equation:

Simplifying
w2 + -22w = 23

Reorder the terms:
-22w + w2 = 23

Solving
-22w + w2 = 23

Solving for variable 'w'.

Reorder the terms:
-23 + -22w + w2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + -22w + w2 = 0

Factor a trinomial.
(-1 + -1w)(23 + -1w) = 0

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 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 + -1w = 0 + 1

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

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

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

Simplifying
w = -1
Subproblem 2
Set the factor '(23 + -1w)' equal to zero and attempt to solve:

Simplifying
23 + -1w = 0

Solving
23 + -1w = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1w = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1w = 0 + -23
-1w = 0 + -23

Combine like terms: 0 + -23 = -23
-1w = -23

Divide each side by '-1'.
w = 23

Simplifying
w = 23
Solution
w = {-1, 23}