5p(2p+1)=6+9

Solution for 5p(2p+1)=6+9 equation:

Simplifying
5p(2p + 1) = 6 + 9

Reorder the terms:
5p(1 + 2p) = 6 + 9
(1 * 5p + 2p * 5p) = 6 + 9
(5p + 10p2) = 6 + 9

Combine like terms: 6 + 9 = 15
5p + 10p2 = 15

Solving
5p + 10p2 = 15

Solving for variable 'p'.

Reorder the terms:
-15 + 5p + 10p2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 5p + 10p2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + p + 2p2) = 0

Factor a trinomial.
5((-3 + -2p)(1 + -1p)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + -2p)' equal to zero and attempt to solve:

Simplifying
-3 + -2p = 0

Solving
-3 + -2p = 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 + -2p = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2p = 0 + 3
-2p = 0 + 3

Combine like terms: 0 + 3 = 3
-2p = 3

Divide each side by '-2'.
p = -1.5

Simplifying
p = -1.5
Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve:

Simplifying
1 + -1p = 0

Solving
1 + -1p = 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 + -1p = 0 + -1

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

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

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

Simplifying
p = 1
Solution
p = {-1.5, 1}