0=3y^2+18y+54

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Solution for 0=3y^2+18y+54 equation:


Simplifying
0 = 3y2 + 18y + 54

Reorder the terms:
0 = 54 + 18y + 3y2

Solving
0 = 54 + 18y + 3y2

Solving for variable 'y'.

Combine like terms: 0 + -54 = -54
-54 + -18y + -3y2 = 54 + 18y + 3y2 + -54 + -18y + -3y2

Reorder the terms:
-54 + -18y + -3y2 = 54 + -54 + 18y + -18y + 3y2 + -3y2

Combine like terms: 54 + -54 = 0
-54 + -18y + -3y2 = 0 + 18y + -18y + 3y2 + -3y2
-54 + -18y + -3y2 = 18y + -18y + 3y2 + -3y2

Combine like terms: 18y + -18y = 0
-54 + -18y + -3y2 = 0 + 3y2 + -3y2
-54 + -18y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-54 + -18y + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(18 + 6y + y2) = 0

Ignore the factor -3.

Subproblem 1

Set the factor '(18 + 6y + y2)' equal to zero and attempt to solve: Simplifying 18 + 6y + y2 = 0 Solving 18 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 6y + -18 + y2 = 0 + -18 Reorder the terms: 18 + -18 + 6y + y2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 6y + y2 = 0 + -18 6y + y2 = 0 + -18 Combine like terms: 0 + -18 = -18 6y + y2 = -18 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -18 + 9 Reorder the terms: 9 + 6y + y2 = -18 + 9 Combine like terms: -18 + 9 = -9 9 + 6y + y2 = -9 Factor a perfect square on the left side: (y + 3)(y + 3) = -9 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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