5p^2=300+20p

Solution for 5p^2=300+20p equation:

Simplifying
5p2 = 300 + 20p

Solving
5p2 = 300 + 20p

Solving for variable 'p'.

Reorder the terms:
-300 + -20p + 5p2 = 300 + 20p + -300 + -20p

Reorder the terms:
-300 + -20p + 5p2 = 300 + -300 + 20p + -20p

Combine like terms: 300 + -300 = 0
-300 + -20p + 5p2 = 0 + 20p + -20p
-300 + -20p + 5p2 = 20p + -20p

Combine like terms: 20p + -20p = 0
-300 + -20p + 5p2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-60 + -4p + p2) = 0

Factor a trinomial.
5((-6 + -1p)(10 + -1p)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -1p)' equal to zero and attempt to solve:

Simplifying
-6 + -1p = 0

Solving
-6 + -1p = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1p = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1p = 0 + 6
-1p = 0 + 6

Combine like terms: 0 + 6 = 6
-1p = 6

Divide each side by '-1'.
p = -6

Simplifying
p = -6
Subproblem 2
Set the factor '(10 + -1p)' equal to zero and attempt to solve:

Simplifying
10 + -1p = 0

Solving
10 + -1p = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1p = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1p = 0 + -10
-1p = 0 + -10

Combine like terms: 0 + -10 = -10
-1p = -10

Divide each side by '-1'.
p = 10

Simplifying
p = 10
Solution
p = {-6, 10}