4+16p+16p^2-36p=0

Solution for 4+16p+16p^2-36p=0 equation:

Simplifying
4 + 16p + 16p2 + -36p = 0

Reorder the terms:
4 + 16p + -36p + 16p2 = 0

Combine like terms: 16p + -36p = -20p
4 + -20p + 16p2 = 0

Solving
4 + -20p + 16p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -5p + 4p2) = 0

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

Ignore the factor 4.
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 '(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 = {0.25, 1}