5p^2+p+3=9

Solution for 5p^2+p+3=9 equation:

Simplifying
5p2 + p + 3 = 9

Reorder the terms:
3 + p + 5p2 = 9

Solving
3 + p + 5p2 = 9

Solving for variable 'p'.

Reorder the terms:
3 + -9 + p + 5p2 = 9 + -9

Combine like terms: 3 + -9 = -6
-6 + p + 5p2 = 9 + -9

Combine like terms: 9 + -9 = 0
-6 + p + 5p2 = 0

Factor a trinomial.
(-6 + -5p)(1 + -1p) = 0

Subproblem 1
Set the factor '(-6 + -5p)' equal to zero and attempt to solve:

Simplifying
-6 + -5p = 0

Solving
-6 + -5p = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5p = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5p = 0 + 6
-5p = 0 + 6

Combine like terms: 0 + 6 = 6
-5p = 6

Divide each side by '-5'.
p = -1.2

Simplifying
p = -1.2
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 = {-1.2, 1}