0=w^2-88w+1407

Solution for 0=w^2-88w+1407 equation:

Simplifying
0 = w2 + -88w + 1407

Reorder the terms:
0 = 1407 + -88w + w2

Solving
0 = 1407 + -88w + w2

Solving for variable 'w'.

Combine like terms: 0 + -1407 = -1407
-1407 + 88w + -1w2 = 1407 + -88w + w2 + -1407 + 88w + -1w2

Reorder the terms:
-1407 + 88w + -1w2 = 1407 + -1407 + -88w + 88w + w2 + -1w2

Combine like terms: 1407 + -1407 = 0
-1407 + 88w + -1w2 = 0 + -88w + 88w + w2 + -1w2
-1407 + 88w + -1w2 = -88w + 88w + w2 + -1w2

Combine like terms: -88w + 88w = 0
-1407 + 88w + -1w2 = 0 + w2 + -1w2
-1407 + 88w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-1407 + 88w + -1w2 = 0

Factor a trinomial.
(-67 + w)(21 + -1w) = 0

Subproblem 1
Set the factor '(-67 + w)' equal to zero and attempt to solve:

Simplifying
-67 + w = 0

Solving
-67 + w = 0

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

Add '67' to each side of the equation.
-67 + 67 + w = 0 + 67

Combine like terms: -67 + 67 = 0
0 + w = 0 + 67
w = 0 + 67

Combine like terms: 0 + 67 = 67
w = 67

Simplifying
w = 67
Subproblem 2
Set the factor '(21 + -1w)' equal to zero and attempt to solve:

Simplifying
21 + -1w = 0

Solving
21 + -1w = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1w = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1w = 0 + -21
-1w = 0 + -21

Combine like terms: 0 + -21 = -21
-1w = -21

Divide each side by '-1'.
w = 21

Simplifying
w = 21
Solution
w = {67, 21}