24y^2=3-14y

Solution for 24y^2=3-14y equation:

Simplifying
24y2 = 3 + -14y

Solving
24y2 = 3 + -14y

Solving for variable 'y'.

Reorder the terms:
-3 + 14y + 24y2 = 3 + -14y + -3 + 14y

Reorder the terms:
-3 + 14y + 24y2 = 3 + -3 + -14y + 14y

Combine like terms: 3 + -3 = 0
-3 + 14y + 24y2 = 0 + -14y + 14y
-3 + 14y + 24y2 = -14y + 14y

Combine like terms: -14y + 14y = 0
-3 + 14y + 24y2 = 0

Factor a trinomial.
(-3 + -4y)(1 + -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 '(1 + -6y)' equal to zero and attempt to solve:

Simplifying
1 + -6y = 0

Solving
1 + -6y = 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 + -6y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6y = 0 + -1
-6y = 0 + -1

Combine like terms: 0 + -1 = -1
-6y = -1

Divide each side by '-6'.
y = 0.1666666667

Simplifying
y = 0.1666666667
Solution
y = {-0.75, 0.1666666667}