4p(2p+3)=36

Solution for 4p(2p+3)=36 equation:

Simplifying
4p(2p + 3) = 36

Reorder the terms:
4p(3 + 2p) = 36
(3 * 4p + 2p * 4p) = 36
(12p + 8p2) = 36

Solving
12p + 8p2 = 36

Solving for variable 'p'.

Reorder the terms:
-36 + 12p + 8p2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 12p + 8p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + 3p + 2p2) = 0

Factor a trinomial.
4((-3 + -1p)(3 + -2p)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
p = {-3, 1.5}