5p^2=18p-9

Solution for 5p^2=18p-9 equation:

Simplifying
5p2 = 18p + -9

Reorder the terms:
5p2 = -9 + 18p

Solving
5p2 = -9 + 18p

Solving for variable 'p'.

Reorder the terms:
9 + -18p + 5p2 = -9 + 18p + 9 + -18p

Reorder the terms:
9 + -18p + 5p2 = -9 + 9 + 18p + -18p

Combine like terms: -9 + 9 = 0
9 + -18p + 5p2 = 0 + 18p + -18p
9 + -18p + 5p2 = 18p + -18p

Combine like terms: 18p + -18p = 0
9 + -18p + 5p2 = 0

Factor a trinomial.
(3 + -5p)(3 + -1p) = 0

Subproblem 1
Set the factor '(3 + -5p)' equal to zero and attempt to solve:

Simplifying
3 + -5p = 0

Solving
3 + -5p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5p = 0 + -3
-5p = 0 + -3

Combine like terms: 0 + -3 = -3
-5p = -3

Divide each side by '-5'.
p = 0.6

Simplifying
p = 0.6
Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {0.6, 3}