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

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

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

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

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

Combine like terms: 24y + -7y = 17y
(-42 + 17y + 4y2) = 0

Solving
-42 + 17y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + -1y)(7 + -4y) = 0

Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(7 + -4y)' equal to zero and attempt to solve:

Simplifying
7 + -4y = 0

Solving
7 + -4y = 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 + -4y = 0 + -7

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

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

Divide each side by '-4'.
y = 1.75

Simplifying
y = 1.75
Solution
y = {-6, 1.75}