(6y-3)(7y-4)=

Solution for (6y-3)(7y-4)= equation:

Simplifying
(6y + -3)(7y + -4) = 0

Reorder the terms:
(-3 + 6y)(7y + -4) = 0

Reorder the terms:
(-3 + 6y)(-4 + 7y) = 0

Multiply (-3 + 6y) * (-4 + 7y)
(-3(-4 + 7y) + 6y * (-4 + 7y)) = 0
((-4 * -3 + 7y * -3) + 6y * (-4 + 7y)) = 0
((12 + -21y) + 6y * (-4 + 7y)) = 0
(12 + -21y + (-4 * 6y + 7y * 6y)) = 0
(12 + -21y + (-24y + 42y2)) = 0

Combine like terms: -21y + -24y = -45y
(12 + -45y + 42y2) = 0

Solving
12 + -45y + 42y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -15y + 14y2) = 0

Factor a trinomial.
3((1 + -2y)(4 + -7y)) = 0

Ignore the factor 3.
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 '(4 + -7y)' equal to zero and attempt to solve:

Simplifying
4 + -7y = 0

Solving
4 + -7y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7y = 0 + -4
-7y = 0 + -4

Combine like terms: 0 + -4 = -4
-7y = -4

Divide each side by '-7'.
y = 0.5714285714

Simplifying
y = 0.5714285714
Solution
y = {0.5, 0.5714285714}