(y+32)(3y-1)=0

Solution for (y+32)(3y-1)=0 equation:

Simplifying
(y + 32)(3y + -1) = 0

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

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

Multiply (32 + y) * (-1 + 3y)
(32(-1 + 3y) + y(-1 + 3y)) = 0
((-1 * 32 + 3y * 32) + y(-1 + 3y)) = 0
((-32 + 96y) + y(-1 + 3y)) = 0
(-32 + 96y + (-1 * y + 3y * y)) = 0
(-32 + 96y + (-1y + 3y2)) = 0

Combine like terms: 96y + -1y = 95y
(-32 + 95y + 3y2) = 0

Solving
-32 + 95y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-32 + -1y)(1 + -3y) = 0

Subproblem 1
Set the factor '(-32 + -1y)' equal to zero and attempt to solve:

Simplifying
-32 + -1y = 0

Solving
-32 + -1y = 0

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

Add '32' to each side of the equation.
-32 + 32 + -1y = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1y = 0 + 32
-1y = 0 + 32

Combine like terms: 0 + 32 = 32
-1y = 32

Divide each side by '-1'.
y = -32

Simplifying
y = -32
Subproblem 2
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
Solution
y = {-32, 0.3333333333}