5p^2-10p-19=-4

Solution for 5p^2-10p-19=-4 equation:

Simplifying
5p2 + -10p + -19 = -4

Reorder the terms:
-19 + -10p + 5p2 = -4

Solving
-19 + -10p + 5p2 = -4

Solving for variable 'p'.

Reorder the terms:
-19 + 4 + -10p + 5p2 = -4 + 4

Combine like terms: -19 + 4 = -15
-15 + -10p + 5p2 = -4 + 4

Combine like terms: -4 + 4 = 0
-15 + -10p + 5p2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -2p + p2) = 0

Factor a trinomial.
5((-1 + -1p)(3 + -1p)) = 0

Ignore the factor 5.
Subproblem 1
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
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 = {-1, 3}