4y^2=11y-6

Solution for 4y^2=11y-6 equation:

Simplifying
4y2 = 11y + -6

Reorder the terms:
4y2 = -6 + 11y

Solving
4y2 = -6 + 11y

Solving for variable 'y'.

Reorder the terms:
6 + -11y + 4y2 = -6 + 11y + 6 + -11y

Reorder the terms:
6 + -11y + 4y2 = -6 + 6 + 11y + -11y

Combine like terms: -6 + 6 = 0
6 + -11y + 4y2 = 0 + 11y + -11y
6 + -11y + 4y2 = 11y + -11y

Combine like terms: 11y + -11y = 0
6 + -11y + 4y2 = 0

Factor a trinomial.
(3 + -4y)(2 + -1y) = 0

Subproblem 1
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 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 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
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 = {0.75, 2}