w^2-47w+90=0

Solution for w^2-47w+90=0 equation:

Simplifying
w2 + -47w + 90 = 0

Reorder the terms:
90 + -47w + w2 = 0

Solving
90 + -47w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(2 + -1w)(45 + -1w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(45 + -1w)' equal to zero and attempt to solve:

Simplifying
45 + -1w = 0

Solving
45 + -1w = 0

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

Add '-45' to each side of the equation.
45 + -45 + -1w = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -1w = 0 + -45
-1w = 0 + -45

Combine like terms: 0 + -45 = -45
-1w = -45

Divide each side by '-1'.
w = 45

Simplifying
w = 45
Solution
w = {2, 45}