0=24y^2+28y+8

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Solution for 0=24y^2+28y+8 equation: 


Simplifying
0 = 24y2 + 28y + 8

Reorder the terms:
0 = 8 + 28y + 24y2

Solving
0 = 8 + 28y + 24y2

Solving for variable 'y'.

Combine like terms: 0 + -8 = -8
-8 + -28y + -24y2 = 8 + 28y + 24y2 + -8 + -28y + -24y2

Reorder the terms:
-8 + -28y + -24y2 = 8 + -8 + 28y + -28y + 24y2 + -24y2

Combine like terms: 8 + -8 = 0
-8 + -28y + -24y2 = 0 + 28y + -28y + 24y2 + -24y2
-8 + -28y + -24y2 = 28y + -28y + 24y2 + -24y2

Combine like terms: 28y + -28y = 0
-8 + -28y + -24y2 = 0 + 24y2 + -24y2
-8 + -28y + -24y2 = 24y2 + -24y2

Combine like terms: 24y2 + -24y2 = 0
-8 + -28y + -24y2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(2 + 7y + 6y2) = 0

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

Ignore the factor -4.

Subproblem 1
Set the factor '(2 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

Solving
2 + 3y = 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 + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667

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

Simplifying
1 + 2y = 0

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

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

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

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {-0.6666666667, -0.5}

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