(6p+4)(8p-3)=0

Solution for (6p+4)(8p-3)=0 equation:

Simplifying
(6p + 4)(8p + -3) = 0

Reorder the terms:
(4 + 6p)(8p + -3) = 0

Reorder the terms:
(4 + 6p)(-3 + 8p) = 0

Multiply (4 + 6p) * (-3 + 8p)
(4(-3 + 8p) + 6p * (-3 + 8p)) = 0
((-3 * 4 + 8p * 4) + 6p * (-3 + 8p)) = 0
((-12 + 32p) + 6p * (-3 + 8p)) = 0
(-12 + 32p + (-3 * 6p + 8p * 6p)) = 0
(-12 + 32p + (-18p + 48p2)) = 0

Combine like terms: 32p + -18p = 14p
(-12 + 14p + 48p2) = 0

Solving
-12 + 14p + 48p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 7p + 24p2) = 0

Factor a trinomial.
2((-2 + -3p)(3 + -8p)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -3p)' equal to zero and attempt to solve:

Simplifying
-2 + -3p = 0

Solving
-2 + -3p = 0

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

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

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

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

Divide each side by '-3'.
p = -0.6666666667

Simplifying
p = -0.6666666667
Subproblem 2
Set the factor '(3 + -8p)' equal to zero and attempt to solve:

Simplifying
3 + -8p = 0

Solving
3 + -8p = 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 + -8p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8p = 0 + -3
-8p = 0 + -3

Combine like terms: 0 + -3 = -3
-8p = -3

Divide each side by '-8'.
p = 0.375

Simplifying
p = 0.375
Solution
p = {-0.6666666667, 0.375}