12y^2-32y+24=0

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Solution for 12y^2-32y+24=0 equation:


Simplifying
12y2 + -32y + 24 = 0

Reorder the terms:
24 + -32y + 12y2 = 0

Solving
24 + -32y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -8y + 3y2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(6 + -8y + 3y2)' equal to zero and attempt to solve: Simplifying 6 + -8y + 3y2 = 0 Solving 6 + -8y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + -2.666666667y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.666666667y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -2.666666667y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.666666667y + y2 = 0 + -2 -2.666666667y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.666666667y + y2 = -2 The y term is -2.666666667y. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667y + 1.777777780 + y2 = -2 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667y + y2 = -2 + 1.777777780 Combine like terms: -2 + 1.777777780 = -0.22222222 1.777777780 + -2.666666667y + y2 = -0.22222222 Factor a perfect square on the left side: (y + -1.333333334)(y + -1.333333334) = -0.22222222 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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