4y^2=9y-2

Solution for 4y^2=9y-2 equation:

Simplifying
4y2 = 9y + -2

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

Solving
4y2 = -2 + 9y

Solving for variable 'y'.

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

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

Combine like terms: -2 + 2 = 0
2 + -9y + 4y2 = 0 + 9y + -9y
2 + -9y + 4y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
2 + -9y + 4y2 = 0

Factor a trinomial.
(1 + -4y)(2 + -1y) = 0

Subproblem 1
Set the factor '(1 + -4y)' equal to zero and attempt to solve:

Simplifying
1 + -4y = 0

Solving
1 + -4y = 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 + -4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4y = 0 + -1
-4y = 0 + -1

Combine like terms: 0 + -1 = -1
-4y = -1

Divide each side by '-4'.
y = 0.25

Simplifying
y = 0.25
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {0.25, 2}