w^2+4wp-45p^2=0

Solution for w^2+4wp-45p^2=0 equation:

Simplifying
w2 + 4wp + -45p2 = 0

Reorder the terms:
4pw + -45p2 + w2 = 0

Solving
4pw + -45p2 + w2 = 0

Solving for variable 'p'.

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

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

Simplifying
-9p + -1w = 0

Solving
-9p + -1w = 0

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

Add 'w' to each side of the equation.
-9p + -1w + w = 0 + w

Combine like terms: -1w + w = 0
-9p + 0 = 0 + w
-9p = 0 + w
Remove the zero:
-9p = w

Divide each side by '-9'.
p = -0.1111111111w

Simplifying
p = -0.1111111111w
Subproblem 2
Set the factor '(5p + -1w)' equal to zero and attempt to solve:

Simplifying
5p + -1w = 0

Solving
5p + -1w = 0

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

Add 'w' to each side of the equation.
5p + -1w + w = 0 + w

Combine like terms: -1w + w = 0
5p + 0 = 0 + w
5p = 0 + w
Remove the zero:
5p = w

Divide each side by '5'.
p = 0.2w

Simplifying
p = 0.2w
Solution
p = {-0.1111111111w, 0.2w}