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

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

Simplifying
(3y + 4)(y + -1) = -2

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

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

Multiply (4 + 3y) * (-1 + y)
(4(-1 + y) + 3y * (-1 + y)) = -2
((-1 * 4 + y * 4) + 3y * (-1 + y)) = -2
((-4 + 4y) + 3y * (-1 + y)) = -2
(-4 + 4y + (-1 * 3y + y * 3y)) = -2
(-4 + 4y + (-3y + 3y2)) = -2

Combine like terms: 4y + -3y = 1y
(-4 + 1y + 3y2) = -2

Solving
-4 + 1y + 3y2 = -2

Solving for variable 'y'.

Reorder the terms:
-4 + 2 + 1y + 3y2 = -2 + 2

Combine like terms: -4 + 2 = -2
-2 + 1y + 3y2 = -2 + 2

Combine like terms: -2 + 2 = 0
-2 + 1y + 3y2 = 0

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

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 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 + -1y = 0 + 1

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

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

Divide each side by '-1'.
y = -1

Simplifying
y = -1
Subproblem 2
Set the factor '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3y = 0 + -2
-3y = 0 + -2

Combine like terms: 0 + -2 = -2
-3y = -2

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {-1, 0.6666666667}