4p^2-8p-194=-2

Solution for 4p^2-8p-194=-2 equation:

Simplifying
4p2 + -8p + -194 = -2

Reorder the terms:
-194 + -8p + 4p2 = -2

Solving
-194 + -8p + 4p2 = -2

Solving for variable 'p'.

Reorder the terms:
-194 + 2 + -8p + 4p2 = -2 + 2

Combine like terms: -194 + 2 = -192
-192 + -8p + 4p2 = -2 + 2

Combine like terms: -2 + 2 = 0
-192 + -8p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-48 + -2p + p2) = 0

Factor a trinomial.
4((-6 + -1p)(8 + -1p)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + -1p)' equal to zero and attempt to solve:

Simplifying
-6 + -1p = 0

Solving
-6 + -1p = 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 + -1p = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1p = 0 + 6
-1p = 0 + 6

Combine like terms: 0 + 6 = 6
-1p = 6

Divide each side by '-1'.
p = -6

Simplifying
p = -6
Subproblem 2
Set the factor '(8 + -1p)' equal to zero and attempt to solve:

Simplifying
8 + -1p = 0

Solving
8 + -1p = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1p = 0 + -8
-1p = 0 + -8

Combine like terms: 0 + -8 = -8
-1p = -8

Divide each side by '-1'.
p = 8

Simplifying
p = 8
Solution
p = {-6, 8}