3p^2=4p-1

Solution for 3p^2=4p-1 equation:

Simplifying
3p2 = 4p + -1

Reorder the terms:
3p2 = -1 + 4p

Solving
3p2 = -1 + 4p

Solving for variable 'p'.

Reorder the terms:
1 + -4p + 3p2 = -1 + 4p + 1 + -4p

Reorder the terms:
1 + -4p + 3p2 = -1 + 1 + 4p + -4p

Combine like terms: -1 + 1 = 0
1 + -4p + 3p2 = 0 + 4p + -4p
1 + -4p + 3p2 = 4p + -4p

Combine like terms: 4p + -4p = 0
1 + -4p + 3p2 = 0

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

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

Simplifying
1 + -3p = 0

Solving
1 + -3p = 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 + -3p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3p = 0 + -1
-3p = 0 + -1

Combine like terms: 0 + -1 = -1
-3p = -1

Divide each side by '-3'.
p = 0.3333333333

Simplifying
p = 0.3333333333
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 = {0.3333333333, 1}