4p^2=13p-3

Solution for 4p^2=13p-3 equation:

Simplifying
4p2 = 13p + -3

Reorder the terms:
4p2 = -3 + 13p

Solving
4p2 = -3 + 13p

Solving for variable 'p'.

Reorder the terms:
3 + -13p + 4p2 = -3 + 13p + 3 + -13p

Reorder the terms:
3 + -13p + 4p2 = -3 + 3 + 13p + -13p

Combine like terms: -3 + 3 = 0
3 + -13p + 4p2 = 0 + 13p + -13p
3 + -13p + 4p2 = 13p + -13p

Combine like terms: 13p + -13p = 0
3 + -13p + 4p2 = 0

Factor a trinomial.
(1 + -4p)(3 + -1p) = 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 + -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
Solution
p = {0.25, 3}