(3p-2)(3p+4)=0

Solution for (3p-2)(3p+4)=0 equation:

Simplifying
(3p + -2)(3p + 4) = 0

Reorder the terms:
(-2 + 3p)(3p + 4) = 0

Reorder the terms:
(-2 + 3p)(4 + 3p) = 0

Multiply (-2 + 3p) * (4 + 3p)
(-2(4 + 3p) + 3p * (4 + 3p)) = 0
((4 * -2 + 3p * -2) + 3p * (4 + 3p)) = 0
((-8 + -6p) + 3p * (4 + 3p)) = 0
(-8 + -6p + (4 * 3p + 3p * 3p)) = 0
(-8 + -6p + (12p + 9p2)) = 0

Combine like terms: -6p + 12p = 6p
(-8 + 6p + 9p2) = 0

Solving
-8 + 6p + 9p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-4 + -3p)(2 + -3p) = 0

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

Simplifying
-4 + -3p = 0

Solving
-4 + -3p = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3p = 0 + 4
-3p = 0 + 4

Combine like terms: 0 + 4 = 4
-3p = 4

Divide each side by '-3'.
p = -1.333333333

Simplifying
p = -1.333333333
Subproblem 2
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
Solution
p = {-1.333333333, 0.6666666667}