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

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

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

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

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

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

Combine like terms: -18y + 7y = -11y
(-42 + -11y + 3y2) = 0

Solving
-42 + -11y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -3y)(6 + -1y) = 0

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

Simplifying
-7 + -3y = 0

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

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

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

Divide each side by '-3'.
y = -2.333333333

Simplifying
y = -2.333333333
Subproblem 2
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
Solution
y = {-2.333333333, 6}