5p^2=2+9p

Solution for 5p^2=2+9p equation:

Simplifying
5p2 = 2 + 9p

Solving
5p2 = 2 + 9p

Solving for variable 'p'.

Reorder the terms:
-2 + -9p + 5p2 = 2 + 9p + -2 + -9p

Reorder the terms:
-2 + -9p + 5p2 = 2 + -2 + 9p + -9p

Combine like terms: 2 + -2 = 0
-2 + -9p + 5p2 = 0 + 9p + -9p
-2 + -9p + 5p2 = 9p + -9p

Combine like terms: 9p + -9p = 0
-2 + -9p + 5p2 = 0

Factor a trinomial.
(-1 + -5p)(2 + -1p) = 0

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

Simplifying
-1 + -5p = 0

Solving
-1 + -5p = 0

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

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

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

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

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

Simplifying
p = -0.2
Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {-0.2, 2}