2y^2+7y-9=0

Solution for 2y^2+7y-9=0 equation:

Simplifying
2y2 + 7y + -9 = 0

Reorder the terms:
-9 + 7y + 2y2 = 0

Solving
-9 + 7y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-9 + -2y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-9 + -2y)' equal to zero and attempt to solve:

Simplifying
-9 + -2y = 0

Solving
-9 + -2y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2y = 0 + 9
-2y = 0 + 9

Combine like terms: 0 + 9 = 9
-2y = 9

Divide each side by '-2'.
y = -4.5

Simplifying
y = -4.5
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 = {-4.5, 1}