24y^2=1-2y

Solution for 24y^2=1-2y equation:

Simplifying
24y2 = 1 + -2y

Solving
24y2 = 1 + -2y

Solving for variable 'y'.

Reorder the terms:
-1 + 2y + 24y2 = 1 + -2y + -1 + 2y

Reorder the terms:
-1 + 2y + 24y2 = 1 + -1 + -2y + 2y

Combine like terms: 1 + -1 = 0
-1 + 2y + 24y2 = 0 + -2y + 2y
-1 + 2y + 24y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-1 + 2y + 24y2 = 0

Factor a trinomial.
(-1 + -4y)(1 + -6y) = 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 '(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 = {-0.25, 0.1666666667}