4p^2=12p-5

Solution for 4p^2=12p-5 equation:

Simplifying
4p2 = 12p + -5

Reorder the terms:
4p2 = -5 + 12p

Solving
4p2 = -5 + 12p

Solving for variable 'p'.

Reorder the terms:
5 + -12p + 4p2 = -5 + 12p + 5 + -12p

Reorder the terms:
5 + -12p + 4p2 = -5 + 5 + 12p + -12p

Combine like terms: -5 + 5 = 0
5 + -12p + 4p2 = 0 + 12p + -12p
5 + -12p + 4p2 = 12p + -12p

Combine like terms: 12p + -12p = 0
5 + -12p + 4p2 = 0

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

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

Simplifying
1 + -2p = 0

Solving
1 + -2p = 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 + -2p = 0 + -1

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

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

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
Subproblem 2
Set the factor '(5 + -2p)' equal to zero and attempt to solve:

Simplifying
5 + -2p = 0

Solving
5 + -2p = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2p = 0 + -5

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

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

Divide each side by '-2'.
p = 2.5

Simplifying
p = 2.5
Solution
p = {0.5, 2.5}