(8y-3)(2y+1)=0

Solution for (8y-3)(2y+1)=0 equation:

Simplifying
(8y + -3)(2y + 1) = 0

Reorder the terms:
(-3 + 8y)(2y + 1) = 0

Reorder the terms:
(-3 + 8y)(1 + 2y) = 0

Multiply (-3 + 8y) * (1 + 2y)
(-3(1 + 2y) + 8y * (1 + 2y)) = 0
((1 * -3 + 2y * -3) + 8y * (1 + 2y)) = 0
((-3 + -6y) + 8y * (1 + 2y)) = 0
(-3 + -6y + (1 * 8y + 2y * 8y)) = 0
(-3 + -6y + (8y + 16y2)) = 0

Combine like terms: -6y + 8y = 2y
(-3 + 2y + 16y2) = 0

Solving
-3 + 2y + 16y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -2y)(3 + -8y) = 0

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

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 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 + -2y = 0 + 1

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

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

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

Simplifying
y = -0.5
Subproblem 2
Set the factor '(3 + -8y)' equal to zero and attempt to solve:

Simplifying
3 + -8y = 0

Solving
3 + -8y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -8y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8y = 0 + -3
-8y = 0 + -3

Combine like terms: 0 + -3 = -3
-8y = -3

Divide each side by '-8'.
y = 0.375

Simplifying
y = 0.375
Solution
y = {-0.5, 0.375}