5p^2-2p-7=0

Solution for 5p^2-2p-7=0 equation:

Simplifying
5p2 + -2p + -7 = 0

Reorder the terms:
-7 + -2p + 5p2 = 0

Solving
-7 + -2p + 5p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-1 + -1p)(7 + -5p) = 0

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 '(7 + -5p)' equal to zero and attempt to solve:

Simplifying
7 + -5p = 0

Solving
7 + -5p = 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 + -5p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5p = 0 + -7
-5p = 0 + -7

Combine like terms: 0 + -7 = -7
-5p = -7

Divide each side by '-5'.
p = 1.4

Simplifying
p = 1.4
Solution
p = {-1, 1.4}