(7-y)(4y-6)=0

Solution for (7-y)(4y-6)=0 equation:

Simplifying
(7 + -1y)(4y + -6) = 0

Reorder the terms:
(7 + -1y)(-6 + 4y) = 0

Multiply (7 + -1y) * (-6 + 4y)
(7(-6 + 4y) + -1y * (-6 + 4y)) = 0
((-6 * 7 + 4y * 7) + -1y * (-6 + 4y)) = 0
((-42 + 28y) + -1y * (-6 + 4y)) = 0
(-42 + 28y + (-6 * -1y + 4y * -1y)) = 0
(-42 + 28y + (6y + -4y2)) = 0

Combine like terms: 28y + 6y = 34y
(-42 + 34y + -4y2) = 0

Solving
-42 + 34y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 17y + -2y2) = 0

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

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

Simplifying
-7 + y = 0

Solving
-7 + y = 0

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

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

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

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

Simplifying
y = 7
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 = {7, 1.5}