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

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

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

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

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

Combine like terms: p + 3p = 4p
(1 + p)(-2 + 4p) = 0

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

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

Solving
-2 + 2p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + p + 2p2) = 0

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

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

Simplifying
1 + -2p = 0

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

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

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

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
Solution
p = {-1, 0.5}