4p^2=3+11p

Solution for 4p^2=3+11p equation:

Simplifying
4p2 = 3 + 11p

Solving
4p2 = 3 + 11p

Solving for variable 'p'.

Reorder the terms:
-3 + -11p + 4p2 = 3 + 11p + -3 + -11p

Reorder the terms:
-3 + -11p + 4p2 = 3 + -3 + 11p + -11p

Combine like terms: 3 + -3 = 0
-3 + -11p + 4p2 = 0 + 11p + -11p
-3 + -11p + 4p2 = 11p + -11p

Combine like terms: 11p + -11p = 0
-3 + -11p + 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}