5w+w^2-150=0

Solution for 5w+w^2-150=0 equation:

Simplifying
5w + w2 + -150 = 0

Reorder the terms:
-150 + 5w + w2 = 0

Solving
-150 + 5w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-15 + -1w)(10 + -1w) = 0

Subproblem 1
Set the factor '(-15 + -1w)' equal to zero and attempt to solve:

Simplifying
-15 + -1w = 0

Solving
-15 + -1w = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1w = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1w = 0 + 15
-1w = 0 + 15

Combine like terms: 0 + 15 = 15
-1w = 15

Divide each side by '-1'.
w = -15

Simplifying
w = -15
Subproblem 2
Set the factor '(10 + -1w)' equal to zero and attempt to solve:

Simplifying
10 + -1w = 0

Solving
10 + -1w = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1w = 0 + -10
-1w = 0 + -10

Combine like terms: 0 + -10 = -10
-1w = -10

Divide each side by '-1'.
w = 10

Simplifying
w = 10
Solution
w = {-15, 10}