2p^2-8p=10

Solution for 2p^2-8p=10 equation:

Simplifying
2p2 + -8p = 10

Reorder the terms:
-8p + 2p2 = 10

Solving
-8p + 2p2 = 10

Solving for variable 'p'.

Reorder the terms:
-10 + -8p + 2p2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -8p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4p + p2) = 0

Factor a trinomial.
2((-1 + -1p)(5 + -1p)) = 0

Ignore the factor 2.
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 '(5 + -1p)' equal to zero and attempt to solve:

Simplifying
5 + -1p = 0

Solving
5 + -1p = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1p = 0 + -5
-1p = 0 + -5

Combine like terms: 0 + -5 = -5
-1p = -5

Divide each side by '-1'.
p = 5

Simplifying
p = 5
Solution
p = {-1, 5}