3(3Y-5)Y=-15

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Solution for 3(3Y-5)Y=-15 equation:


Simplifying
3(3Y + -5) * Y = -15

Reorder the terms:
3(-5 + 3Y) * Y = -15

Reorder the terms for easier multiplication:
3Y(-5 + 3Y) = -15
(-5 * 3Y + 3Y * 3Y) = -15
(-15Y + 9Y2) = -15

Solving
-15Y + 9Y2 = -15

Solving for variable 'Y'.

Reorder the terms:
15 + -15Y + 9Y2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -15Y + 9Y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -5Y + 3Y2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + -5Y + 3Y2)' equal to zero and attempt to solve: Simplifying 5 + -5Y + 3Y2 = 0 Solving 5 + -5Y + 3Y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -1.666666667Y + Y2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667Y + -1.666666667 + Y2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1.666666667Y + Y2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1.666666667Y + Y2 = 0 + -1.666666667 -1.666666667Y + Y2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1.666666667Y + Y2 = -1.666666667 The Y term is -1.666666667Y. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667Y + 0.6944444447 + Y2 = -1.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667Y + Y2 = -1.666666667 + 0.6944444447 Combine like terms: -1.666666667 + 0.6944444447 = -0.9722222223 0.6944444447 + -1.666666667Y + Y2 = -0.9722222223 Factor a perfect square on the left side: (Y + -0.8333333335)(Y + -0.8333333335) = -0.9722222223 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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