8y^2+12y+24=0

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Solution for 8y^2+12y+24=0 equation:


Simplifying
8y2 + 12y + 24 = 0

Reorder the terms:
24 + 12y + 8y2 = 0

Solving
24 + 12y + 8y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 3y + 2y2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(6 + 3y + 2y2)' equal to zero and attempt to solve: Simplifying 6 + 3y + 2y2 = 0 Solving 6 + 3y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 1.5y + y2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1.5y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + 1.5y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1.5y + y2 = 0 + -3 1.5y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 1.5y + y2 = -3 The y term is 1.5y. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5y + 0.5625 + y2 = -3 + 0.5625 Reorder the terms: 0.5625 + 1.5y + y2 = -3 + 0.5625 Combine like terms: -3 + 0.5625 = -2.4375 0.5625 + 1.5y + y2 = -2.4375 Factor a perfect square on the left side: (y + 0.75)(y + 0.75) = -2.4375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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