12p^2-45p-9=3

Solution for 12p^2-45p-9=3 equation:

Simplifying
12p2 + -45p + -9 = 3

Reorder the terms:
-9 + -45p + 12p2 = 3

Solving
-9 + -45p + 12p2 = 3

Solving for variable 'p'.

Reorder the terms:
-9 + -3 + -45p + 12p2 = 3 + -3

Combine like terms: -9 + -3 = -12
-12 + -45p + 12p2 = 3 + -3

Combine like terms: 3 + -3 = 0
-12 + -45p + 12p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -15p + 4p2) = 0

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

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

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

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

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

Divide each side by '-1'.
p = 4

Simplifying
p = 4
Solution
p = {-0.25, 4}