10p^2-1=3p

Solution for 10p^2-1=3p equation:

Simplifying
10p2 + -1 = 3p

Reorder the terms:
-1 + 10p2 = 3p

Solving
-1 + 10p2 = 3p

Solving for variable 'p'.

Reorder the terms:
-1 + -3p + 10p2 = 3p + -3p

Combine like terms: 3p + -3p = 0
-1 + -3p + 10p2 = 0

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

Subproblem 1
Set the factor '(-1 + -5p)' equal to zero and attempt to solve:

Simplifying
-1 + -5p = 0

Solving
-1 + -5p = 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 + -5p = 0 + 1

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

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

Divide each side by '-5'.
p = -0.2

Simplifying
p = -0.2
Subproblem 2
Set the factor '(1 + -2p)' equal to zero and attempt to solve:

Simplifying
1 + -2p = 0

Solving
1 + -2p = 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 + -2p = 0 + -1

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

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

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
Solution
p = {-0.2, 0.5}