0=w^2-169w+4060

Solution for 0=w^2-169w+4060 equation:

Simplifying
0 = w2 + -169w + 4060

Reorder the terms:
0 = 4060 + -169w + w2

Solving
0 = 4060 + -169w + w2

Solving for variable 'w'.

Combine like terms: 0 + -4060 = -4060
-4060 + 169w + -1w2 = 4060 + -169w + w2 + -4060 + 169w + -1w2

Reorder the terms:
-4060 + 169w + -1w2 = 4060 + -4060 + -169w + 169w + w2 + -1w2

Combine like terms: 4060 + -4060 = 0
-4060 + 169w + -1w2 = 0 + -169w + 169w + w2 + -1w2
-4060 + 169w + -1w2 = -169w + 169w + w2 + -1w2

Combine like terms: -169w + 169w = 0
-4060 + 169w + -1w2 = 0 + w2 + -1w2
-4060 + 169w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-4060 + 169w + -1w2 = 0

Factor a trinomial.
(-140 + w)(29 + -1w) = 0

Subproblem 1
Set the factor '(-140 + w)' equal to zero and attempt to solve:

Simplifying
-140 + w = 0

Solving
-140 + w = 0

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

Add '140' to each side of the equation.
-140 + 140 + w = 0 + 140

Combine like terms: -140 + 140 = 0
0 + w = 0 + 140
w = 0 + 140

Combine like terms: 0 + 140 = 140
w = 140

Simplifying
w = 140
Subproblem 2
Set the factor '(29 + -1w)' equal to zero and attempt to solve:

Simplifying
29 + -1w = 0

Solving
29 + -1w = 0

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

Add '-29' to each side of the equation.
29 + -29 + -1w = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -1w = 0 + -29
-1w = 0 + -29

Combine like terms: 0 + -29 = -29
-1w = -29

Divide each side by '-1'.
w = 29

Simplifying
w = 29
Solution
w = {140, 29}