(y-7)(6y+19)=0

Solution for (y-7)(6y+19)=0 equation:

Simplifying
(y + -7)(6y + 19) = 0

Reorder the terms:
(-7 + y)(6y + 19) = 0

Reorder the terms:
(-7 + y)(19 + 6y) = 0

Multiply (-7 + y) * (19 + 6y)
(-7(19 + 6y) + y(19 + 6y)) = 0
((19 * -7 + 6y * -7) + y(19 + 6y)) = 0
((-133 + -42y) + y(19 + 6y)) = 0
(-133 + -42y + (19 * y + 6y * y)) = 0
(-133 + -42y + (19y + 6y2)) = 0

Combine like terms: -42y + 19y = -23y
(-133 + -23y + 6y2) = 0

Solving
-133 + -23y + 6y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-19 + -6y)(7 + -1y) = 0

Subproblem 1
Set the factor '(-19 + -6y)' equal to zero and attempt to solve:

Simplifying
-19 + -6y = 0

Solving
-19 + -6y = 0

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

Add '19' to each side of the equation.
-19 + 19 + -6y = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -6y = 0 + 19
-6y = 0 + 19

Combine like terms: 0 + 19 = 19
-6y = 19

Divide each side by '-6'.
y = -3.166666667

Simplifying
y = -3.166666667
Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

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

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

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

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-3.166666667, 7}