25w+2w^2=75

Solution for 25w+2w^2=75 equation:

Simplifying
25w + 2w2 = 75

Solving
25w + 2w2 = 75

Solving for variable 'w'.

Reorder the terms:
-75 + 25w + 2w2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + 25w + 2w2 = 0

Factor a trinomial.
(-15 + -1w)(5 + -2w) = 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 '(5 + -2w)' equal to zero and attempt to solve:

Simplifying
5 + -2w = 0

Solving
5 + -2w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2w = 0 + -5
-2w = 0 + -5

Combine like terms: 0 + -5 = -5
-2w = -5

Divide each side by '-2'.
w = 2.5

Simplifying
w = 2.5
Solution
w = {-15, 2.5}