5w^2-16w-45=0

Solution for 5w^2-16w-45=0 equation:

Simplifying
5w2 + -16w + -45 = 0

Reorder the terms:
-45 + -16w + 5w2 = 0

Solving
-45 + -16w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + -5w)(5 + -1w) = 0

Subproblem 1
Set the factor '(-9 + -5w)' equal to zero and attempt to solve:

Simplifying
-9 + -5w = 0

Solving
-9 + -5w = 0

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

Add '9' to each side of the equation.
-9 + 9 + -5w = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5w = 0 + 9
-5w = 0 + 9

Combine like terms: 0 + 9 = 9
-5w = 9

Divide each side by '-5'.
w = -1.8

Simplifying
w = -1.8
Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 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 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-1.8, 5}