(8y-6)(3+7y)=0

Solution for (8y-6)(3+7y)=0 equation:

Simplifying
(8y + -6)(3 + 7y) = 0

Reorder the terms:
(-6 + 8y)(3 + 7y) = 0

Multiply (-6 + 8y) * (3 + 7y)
(-6(3 + 7y) + 8y * (3 + 7y)) = 0
((3 * -6 + 7y * -6) + 8y * (3 + 7y)) = 0
((-18 + -42y) + 8y * (3 + 7y)) = 0
(-18 + -42y + (3 * 8y + 7y * 8y)) = 0
(-18 + -42y + (24y + 56y2)) = 0

Combine like terms: -42y + 24y = -18y
(-18 + -18y + 56y2) = 0

Solving
-18 + -18y + 56y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -9y + 28y2) = 0

Factor a trinomial.
2((-3 + -7y)(3 + -4y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -7y)' equal to zero and attempt to solve:

Simplifying
-3 + -7y = 0

Solving
-3 + -7y = 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 + -7y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7y = 0 + 3
-7y = 0 + 3

Combine like terms: 0 + 3 = 3
-7y = 3

Divide each side by '-7'.
y = -0.4285714286

Simplifying
y = -0.4285714286
Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 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 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
Solution
y = {-0.4285714286, 0.75}