6y(y-5)=18-2y

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Solution for 6y(y-5)=18-2y equation:


Simplifying
6y(y + -5) = 18 + -2y

Reorder the terms:
6y(-5 + y) = 18 + -2y
(-5 * 6y + y * 6y) = 18 + -2y
(-30y + 6y2) = 18 + -2y

Solving
-30y + 6y2 = 18 + -2y

Solving for variable 'y'.

Reorder the terms:
-18 + -30y + 2y + 6y2 = 18 + -2y + -18 + 2y

Combine like terms: -30y + 2y = -28y
-18 + -28y + 6y2 = 18 + -2y + -18 + 2y

Reorder the terms:
-18 + -28y + 6y2 = 18 + -18 + -2y + 2y

Combine like terms: 18 + -18 = 0
-18 + -28y + 6y2 = 0 + -2y + 2y
-18 + -28y + 6y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-18 + -28y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -14y + 3y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + -14y + 3y2)' equal to zero and attempt to solve: Simplifying -9 + -14y + 3y2 = 0 Solving -9 + -14y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -4.666666667y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4.666666667y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + -4.666666667y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4.666666667y + y2 = 0 + 3 -4.666666667y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4.666666667y + y2 = 3 The y term is -4.666666667y. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667y + 5.444444448 + y2 = 3 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667y + y2 = 3 + 5.444444448 Combine like terms: 3 + 5.444444448 = 8.444444448 5.444444448 + -4.666666667y + y2 = 8.444444448 Factor a perfect square on the left side: (y + -2.333333334)(y + -2.333333334) = 8.444444448 Calculate the square root of the right side: 2.90593263 Break this problem into two subproblems by setting (y + -2.333333334) equal to 2.90593263 and -2.90593263.

Subproblem 1

y + -2.333333334 = 2.90593263 Simplifying y + -2.333333334 = 2.90593263 Reorder the terms: -2.333333334 + y = 2.90593263 Solving -2.333333334 + y = 2.90593263 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + y = 2.90593263 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + y = 2.90593263 + 2.333333334 y = 2.90593263 + 2.333333334 Combine like terms: 2.90593263 + 2.333333334 = 5.239265964 y = 5.239265964 Simplifying y = 5.239265964

Subproblem 2

y + -2.333333334 = -2.90593263 Simplifying y + -2.333333334 = -2.90593263 Reorder the terms: -2.333333334 + y = -2.90593263 Solving -2.333333334 + y = -2.90593263 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + y = -2.90593263 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + y = -2.90593263 + 2.333333334 y = -2.90593263 + 2.333333334 Combine like terms: -2.90593263 + 2.333333334 = -0.572599296 y = -0.572599296 Simplifying y = -0.572599296

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.239265964, -0.572599296}

Solution

y = {5.239265964, -0.572599296}

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