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

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

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

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

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

Multiply (1 + 3y) * (-1 + 4y)
(1(-1 + 4y) + 3y * (-1 + 4y)) = 0
((-1 * 1 + 4y * 1) + 3y * (-1 + 4y)) = 0
((-1 + 4y) + 3y * (-1 + 4y)) = 0
(-1 + 4y + (-1 * 3y + 4y * 3y)) = 0
(-1 + 4y + (-3y + 12y2)) = 0

Combine like terms: 4y + -3y = 1y
(-1 + 1y + 12y2) = 0

Solving
-1 + 1y + 12y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-1 + -3y = 0

Solving
-1 + -3y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3y = 0 + 1
-3y = 0 + 1

Combine like terms: 0 + 1 = 1
-3y = 1

Divide each side by '-3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Subproblem 2
Set the factor '(1 + -4y)' equal to zero and attempt to solve:

Simplifying
1 + -4y = 0

Solving
1 + -4y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4y = 0 + -1
-4y = 0 + -1

Combine like terms: 0 + -1 = -1
-4y = -1

Divide each side by '-4'.
y = 0.25

Simplifying
y = 0.25
Solution
y = {-0.3333333333, 0.25}