(4+2p)(3p-1)=

Solution for (4+2p)(3p-1)= equation:

Simplifying
(4 + 2p)(3p + -1) = 0

Reorder the terms:
(4 + 2p)(-1 + 3p) = 0

Multiply (4 + 2p) * (-1 + 3p)
(4(-1 + 3p) + 2p * (-1 + 3p)) = 0
((-1 * 4 + 3p * 4) + 2p * (-1 + 3p)) = 0
((-4 + 12p) + 2p * (-1 + 3p)) = 0
(-4 + 12p + (-1 * 2p + 3p * 2p)) = 0
(-4 + 12p + (-2p + 6p2)) = 0

Combine like terms: 12p + -2p = 10p
(-4 + 10p + 6p2) = 0

Solving
-4 + 10p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 5p + 3p2) = 0

Factor a trinomial.
2((-2 + -1p)(1 + -3p)) = 0

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

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 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 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

Simplifying
p = -2
Subproblem 2
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
Solution
p = {-2, 0.3333333333}