15p^2+51p+22=4

Solution for 15p^2+51p+22=4 equation:

Simplifying
15p2 + 51p + 22 = 4

Reorder the terms:
22 + 51p + 15p2 = 4

Solving
22 + 51p + 15p2 = 4

Solving for variable 'p'.

Reorder the terms:
22 + -4 + 51p + 15p2 = 4 + -4

Combine like terms: 22 + -4 = 18
18 + 51p + 15p2 = 4 + -4

Combine like terms: 4 + -4 = 0
18 + 51p + 15p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 17p + 5p2) = 0

Factor a trinomial.
3((3 + p)(2 + 5p)) = 0

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

Simplifying
3 + p = 0

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

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

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

Simplifying
p = -3
Subproblem 2
Set the factor '(2 + 5p)' equal to zero and attempt to solve:

Simplifying
2 + 5p = 0

Solving
2 + 5p = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5p = 0 + -2
5p = 0 + -2

Combine like terms: 0 + -2 = -2
5p = -2

Divide each side by '5'.
p = -0.4

Simplifying
p = -0.4
Solution
p = {-3, -0.4}