(8p-2)(6p+2)=0

Solution for (8p-2)(6p+2)=0 equation:

Simplifying
(8p + -2)(6p + 2) = 0

Reorder the terms:
(-2 + 8p)(6p + 2) = 0

Reorder the terms:
(-2 + 8p)(2 + 6p) = 0

Multiply (-2 + 8p) * (2 + 6p)
(-2(2 + 6p) + 8p * (2 + 6p)) = 0
((2 * -2 + 6p * -2) + 8p * (2 + 6p)) = 0
((-4 + -12p) + 8p * (2 + 6p)) = 0
(-4 + -12p + (2 * 8p + 6p * 8p)) = 0
(-4 + -12p + (16p + 48p2)) = 0

Combine like terms: -12p + 16p = 4p
(-4 + 4p + 48p2) = 0

Solving
-4 + 4p + 48p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + p + 12p2) = 0

Factor a trinomial.
4((-1 + -3p)(1 + -4p)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -3p)' equal to zero and attempt to solve:

Simplifying
-1 + -3p = 0

Solving
-1 + -3p = 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 + -3p = 0 + 1

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

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

Divide each side by '-3'.
p = -0.3333333333

Simplifying
p = -0.3333333333
Subproblem 2
Set the factor '(1 + -4p)' equal to zero and attempt to solve:

Simplifying
1 + -4p = 0

Solving
1 + -4p = 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 + -4p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4p = 0 + -1
-4p = 0 + -1

Combine like terms: 0 + -1 = -1
-4p = -1

Divide each side by '-4'.
p = 0.25

Simplifying
p = 0.25
Solution
p = {-0.3333333333, 0.25}