24y^2-62y=-33

Solution for 24y^2-62y=-33 equation:

Simplifying
24y2 + -62y = -33

Reorder the terms:
-62y + 24y2 = -33

Solving
-62y + 24y2 = -33

Solving for variable 'y'.

Reorder the terms:
33 + -62y + 24y2 = -33 + 33

Combine like terms: -33 + 33 = 0
33 + -62y + 24y2 = 0

Factor a trinomial.
(3 + -4y)(11 + -6y) = 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 '(11 + -6y)' equal to zero and attempt to solve:

Simplifying
11 + -6y = 0

Solving
11 + -6y = 0

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

Add '-11' to each side of the equation.
11 + -11 + -6y = 0 + -11

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

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

Divide each side by '-6'.
y = 1.833333333

Simplifying
y = 1.833333333
Solution
y = {0.75, 1.833333333}