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

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

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

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

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

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

Combine like terms: -4p + 3p = -1p
(-1 + -1p + 12p2) = 0

Solving
-1 + -1p + 12p2 = 0

Solving for variable 'p'.

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

Subproblem 1
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
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 = {-0.25, 0.3333333333}