21=8p^2-2p

Solution for 21=8p^2-2p equation:

Simplifying
21 = 8p2 + -2p

Reorder the terms:
21 = -2p + 8p2

Solving
21 = -2p + 8p2

Solving for variable 'p'.

Reorder the terms:
21 + 2p + -8p2 = -2p + 2p + 8p2 + -8p2

Combine like terms: -2p + 2p = 0
21 + 2p + -8p2 = 0 + 8p2 + -8p2
21 + 2p + -8p2 = 8p2 + -8p2

Combine like terms: 8p2 + -8p2 = 0
21 + 2p + -8p2 = 0

Factor a trinomial.
(7 + -4p)(3 + 2p) = 0

Subproblem 1
Set the factor '(7 + -4p)' equal to zero and attempt to solve:

Simplifying
7 + -4p = 0

Solving
7 + -4p = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4p = 0 + -7
-4p = 0 + -7

Combine like terms: 0 + -7 = -7
-4p = -7

Divide each side by '-4'.
p = 1.75

Simplifying
p = 1.75
Subproblem 2
Set the factor '(3 + 2p)' equal to zero and attempt to solve:

Simplifying
3 + 2p = 0

Solving
3 + 2p = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2p = 0 + -3
2p = 0 + -3

Combine like terms: 0 + -3 = -3
2p = -3

Divide each side by '2'.
p = -1.5

Simplifying
p = -1.5
Solution
p = {1.75, -1.5}