(7y-1)(2y-3)=0

Solution for (7y-1)(2y-3)=0 equation:

Simplifying
(7y + -1)(2y + -3) = 0

Reorder the terms:
(-1 + 7y)(2y + -3) = 0

Reorder the terms:
(-1 + 7y)(-3 + 2y) = 0

Multiply (-1 + 7y) * (-3 + 2y)
(-1(-3 + 2y) + 7y * (-3 + 2y)) = 0
((-3 * -1 + 2y * -1) + 7y * (-3 + 2y)) = 0
((3 + -2y) + 7y * (-3 + 2y)) = 0
(3 + -2y + (-3 * 7y + 2y * 7y)) = 0
(3 + -2y + (-21y + 14y2)) = 0

Combine like terms: -2y + -21y = -23y
(3 + -23y + 14y2) = 0

Solving
3 + -23y + 14y2 = 0

Solving for variable 'y'.

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

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

Simplifying
1 + -7y = 0

Solving
1 + -7y = 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 + -7y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7y = 0 + -1
-7y = 0 + -1

Combine like terms: 0 + -1 = -1
-7y = -1

Divide each side by '-7'.
y = 0.1428571429

Simplifying
y = 0.1428571429
Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 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 + -2y = 0 + -3

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

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

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {0.1428571429, 1.5}