7y^2+19y-6=0

Solution for 7y^2+19y-6=0 equation:

Simplifying
7y2 + 19y + -6 = 0

Reorder the terms:
-6 + 19y + 7y2 = 0

Solving
-6 + 19y + 7y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -1y)(2 + -7y) = 0

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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
Subproblem 2
Set the factor '(2 + -7y)' equal to zero and attempt to solve:

Simplifying
2 + -7y = 0

Solving
2 + -7y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7y = 0 + -2

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

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

Divide each side by '-7'.
y = 0.2857142857

Simplifying
y = 0.2857142857
Solution
y = {-3, 0.2857142857}