(9y^2-7y-6)+(3y+8)=7

Solution for (9y^2-7y-6)+(3y+8)=7 equation:

Simplifying
(9y2 + -7y + -6) + (3y + 8) = 7

Reorder the terms:
(-6 + -7y + 9y2) + (3y + 8) = 7

Remove parenthesis around (-6 + -7y + 9y2)
-6 + -7y + 9y2 + (3y + 8) = 7

Reorder the terms:
-6 + -7y + 9y2 + (8 + 3y) = 7

Remove parenthesis around (8 + 3y)
-6 + -7y + 9y2 + 8 + 3y = 7

Reorder the terms:
-6 + 8 + -7y + 3y + 9y2 = 7

Combine like terms: -6 + 8 = 2
2 + -7y + 3y + 9y2 = 7

Combine like terms: -7y + 3y = -4y
2 + -4y + 9y2 = 7

Solving
2 + -4y + 9y2 = 7

Solving for variable 'y'.

Reorder the terms:
2 + -7 + -4y + 9y2 = 7 + -7

Combine like terms: 2 + -7 = -5
-5 + -4y + 9y2 = 7 + -7

Combine like terms: 7 + -7 = 0
-5 + -4y + 9y2 = 0

Factor a trinomial.
(-5 + -9y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-5 + -9y)' equal to zero and attempt to solve:

Simplifying
-5 + -9y = 0

Solving
-5 + -9y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -9y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -9y = 0 + 5
-9y = 0 + 5

Combine like terms: 0 + 5 = 5
-9y = 5

Divide each side by '-9'.
y = -0.5555555556

Simplifying
y = -0.5555555556
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-0.5555555556, 1}