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((-5 + -1p)(1 + -1p)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-5, 1}