3=2p(4p+5)

Solution for 3=2p(4p+5) equation:

Simplifying
3 = 2p(4p + 5)

Reorder the terms:
3 = 2p(5 + 4p)
3 = (5 * 2p + 4p * 2p)
3 = (10p + 8p2)

Solving
3 = 10p + 8p2

Solving for variable 'p'.

Reorder the terms:
3 + -10p + -8p2 = 10p + -10p + 8p2 + -8p2

Combine like terms: 10p + -10p = 0
3 + -10p + -8p2 = 0 + 8p2 + -8p2
3 + -10p + -8p2 = 8p2 + -8p2

Combine like terms: 8p2 + -8p2 = 0
3 + -10p + -8p2 = 0

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

Subproblem 1
Set the factor '(1 + -4p)' equal to zero and attempt to solve:

Simplifying
1 + -4p = 0

Solving
1 + -4p = 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 + -4p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4p = 0 + -1
-4p = 0 + -1

Combine like terms: 0 + -1 = -1
-4p = -1

Divide each side by '-4'.
p = 0.25

Simplifying
p = 0.25
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 = {0.25, -1.5}