2p^2-10p=12

Solution for 2p^2-10p=12 equation:

Simplifying
2p2 + -10p = 12

Reorder the terms:
-10p + 2p2 = 12

Solving
-10p + 2p2 = 12

Solving for variable 'p'.

Reorder the terms:
-12 + -10p + 2p2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -10p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -5p + p2) = 0

Factor a trinomial.
2((-1 + -1p)(6 + -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 '(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
Solution
p = {-1, 6}