28p^2-24=-4p

Solution for 28p^2-24=-4p equation:

Simplifying
28p2 + -24 = -4p

Reorder the terms:
-24 + 28p2 = -4p

Solving
-24 + 28p2 = -4p

Solving for variable 'p'.

Reorder the terms:
-24 + 4p + 28p2 = -4p + 4p

Combine like terms: -4p + 4p = 0
-24 + 4p + 28p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + p + 7p2) = 0

Factor a trinomial.
4((-1 + -1p)(6 + -7p)) = 0

Ignore the factor 4.
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 + -7p)' equal to zero and attempt to solve:

Simplifying
6 + -7p = 0

Solving
6 + -7p = 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 + -7p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7p = 0 + -6
-7p = 0 + -6

Combine like terms: 0 + -6 = -6
-7p = -6

Divide each side by '-7'.
p = 0.8571428571

Simplifying
p = 0.8571428571
Solution
p = {-1, 0.8571428571}