4p^2-p-3=0

Solution for 4p^2-p-3=0 equation:

Simplifying
4p2 + -1p + -3 = 0

Reorder the terms:
-3 + -1p + 4p2 = 0

Solving
-3 + -1p + 4p2 = 0

Solving for variable 'p'.

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

Subproblem 1
Set the factor '(-3 + -4p)' equal to zero and attempt to solve:

Simplifying
-3 + -4p = 0

Solving
-3 + -4p = 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 + -4p = 0 + 3

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

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

Divide each side by '-4'.
p = -0.75

Simplifying
p = -0.75
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 = {-0.75, 1}