6-y^2+3y=9y+9

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Solution for 6-y^2+3y=9y+9 equation:


Simplifying
6 + -1y2 + 3y = 9y + 9

Reorder the terms:
6 + 3y + -1y2 = 9y + 9

Reorder the terms:
6 + 3y + -1y2 = 9 + 9y

Solving
6 + 3y + -1y2 = 9 + 9y

Solving for variable 'y'.

Reorder the terms:
6 + -9 + 3y + -9y + -1y2 = 9 + 9y + -9 + -9y

Combine like terms: 6 + -9 = -3
-3 + 3y + -9y + -1y2 = 9 + 9y + -9 + -9y

Combine like terms: 3y + -9y = -6y
-3 + -6y + -1y2 = 9 + 9y + -9 + -9y

Reorder the terms:
-3 + -6y + -1y2 = 9 + -9 + 9y + -9y

Combine like terms: 9 + -9 = 0
-3 + -6y + -1y2 = 0 + 9y + -9y
-3 + -6y + -1y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
-3 + -6y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 6y + y2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(3 + 6y + y2)' equal to zero and attempt to solve: Simplifying 3 + 6y + y2 = 0 Solving 3 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 6y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + 6y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 6y + y2 = 0 + -3 6y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 6y + y2 = -3 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 = -3 + 9 Reorder the terms: 9 + 6y + y2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + 6y + y2 = 6 Factor a perfect square on the left side: (y + 3)(y + 3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (y + 3) equal to 2.449489743 and -2.449489743.

Subproblem 1

y + 3 = 2.449489743 Simplifying y + 3 = 2.449489743 Reorder the terms: 3 + y = 2.449489743 Solving 3 + y = 2.449489743 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + y = 2.449489743 + -3 y = 2.449489743 + -3 Combine like terms: 2.449489743 + -3 = -0.550510257 y = -0.550510257 Simplifying y = -0.550510257

Subproblem 2

y + 3 = -2.449489743 Simplifying y + 3 = -2.449489743 Reorder the terms: 3 + y = -2.449489743 Solving 3 + y = -2.449489743 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -2.449489743 + -3 Combine like terms: 3 + -3 = 0 0 + y = -2.449489743 + -3 y = -2.449489743 + -3 Combine like terms: -2.449489743 + -3 = -5.449489743 y = -5.449489743 Simplifying y = -5.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.550510257, -5.449489743}

Solution

y = {-0.550510257, -5.449489743}

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