0=100-52w+w^2

Solution for 0=100-52w+w^2 equation:

Simplifying
0 = 100 + -52w + w2

Solving
0 = 100 + -52w + w2

Solving for variable 'w'.

Combine like terms: 0 + -100 = -100
-100 + 52w + -1w2 = 100 + -52w + w2 + -100 + 52w + -1w2

Reorder the terms:
-100 + 52w + -1w2 = 100 + -100 + -52w + 52w + w2 + -1w2

Combine like terms: 100 + -100 = 0
-100 + 52w + -1w2 = 0 + -52w + 52w + w2 + -1w2
-100 + 52w + -1w2 = -52w + 52w + w2 + -1w2

Combine like terms: -52w + 52w = 0
-100 + 52w + -1w2 = 0 + w2 + -1w2
-100 + 52w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-100 + 52w + -1w2 = 0

Factor a trinomial.
(-50 + w)(2 + -1w) = 0

Subproblem 1
Set the factor '(-50 + w)' equal to zero and attempt to solve:

Simplifying
-50 + w = 0

Solving
-50 + w = 0

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

Add '50' to each side of the equation.
-50 + 50 + w = 0 + 50

Combine like terms: -50 + 50 = 0
0 + w = 0 + 50
w = 0 + 50

Combine like terms: 0 + 50 = 50
w = 50

Simplifying
w = 50
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {50, 2}