15w+w^2=1350

Solution for 15w+w^2=1350 equation:

Simplifying
15w + w2 = 1350

Solving
15w + w2 = 1350

Solving for variable 'w'.

Reorder the terms:
-1350 + 15w + w2 = 1350 + -1350

Combine like terms: 1350 + -1350 = 0
-1350 + 15w + w2 = 0

Factor a trinomial.
(-45 + -1w)(30 + -1w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(30 + -1w)' equal to zero and attempt to solve:

Simplifying
30 + -1w = 0

Solving
30 + -1w = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1w = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1w = 0 + -30
-1w = 0 + -30

Combine like terms: 0 + -30 = -30
-1w = -30

Divide each side by '-1'.
w = 30

Simplifying
w = 30
Solution
w = {-45, 30}