(y-6)(2y+7)=0

Solution for (y-6)(2y+7)=0 equation:

Simplifying
(y + -6)(2y + 7) = 0

Reorder the terms:
(-6 + y)(2y + 7) = 0

Reorder the terms:
(-6 + y)(7 + 2y) = 0

Multiply (-6 + y) * (7 + 2y)
(-6(7 + 2y) + y(7 + 2y)) = 0
((7 * -6 + 2y * -6) + y(7 + 2y)) = 0
((-42 + -12y) + y(7 + 2y)) = 0
(-42 + -12y + (7 * y + 2y * y)) = 0
(-42 + -12y + (7y + 2y2)) = 0

Combine like terms: -12y + 7y = -5y
(-42 + -5y + 2y2) = 0

Solving
-42 + -5y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -2y)(6 + -1y) = 0

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

Simplifying
-7 + -2y = 0

Solving
-7 + -2y = 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 + -2y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2y = 0 + 7
-2y = 0 + 7

Combine like terms: 0 + 7 = 7
-2y = 7

Divide each side by '-2'.
y = -3.5

Simplifying
y = -3.5
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 = {-3.5, 6}