2p^2-p=10

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

Simplifying
2p2 + -1p = 10

Reorder the terms:
-1p + 2p2 = 10

Solving
-1p + 2p2 = 10

Solving for variable 'p'.

Reorder the terms:
-10 + -1p + 2p2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -1p + 2p2 = 0

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

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

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

Simplifying
p = -2
Subproblem 2
Set the factor '(5 + -2p)' equal to zero and attempt to solve:

Simplifying
5 + -2p = 0

Solving
5 + -2p = 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 + -2p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2p = 0 + -5
-2p = 0 + -5

Combine like terms: 0 + -5 = -5
-2p = -5

Divide each side by '-2'.
p = 2.5

Simplifying
p = 2.5
Solution
p = {-2, 2.5}