9y^2+12y-336=0

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Solution for 9y^2+12y-336=0 equation:


Simplifying
9y2 + 12y + -336 = 0

Reorder the terms:
-336 + 12y + 9y2 = 0

Solving
-336 + 12y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-112 + 4y + 3y2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-112 + 4y + 3y2)' equal to zero and attempt to solve: Simplifying -112 + 4y + 3y2 = 0 Solving -112 + 4y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -37.33333333 + 1.333333333y + y2 = 0 Move the constant term to the right: Add '37.33333333' to each side of the equation. -37.33333333 + 1.333333333y + 37.33333333 + y2 = 0 + 37.33333333 Reorder the terms: -37.33333333 + 37.33333333 + 1.333333333y + y2 = 0 + 37.33333333 Combine like terms: -37.33333333 + 37.33333333 = 0.00000000 0.00000000 + 1.333333333y + y2 = 0 + 37.33333333 1.333333333y + y2 = 0 + 37.33333333 Combine like terms: 0 + 37.33333333 = 37.33333333 1.333333333y + y2 = 37.33333333 The y term is 1.333333333y. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333y + 0.4444444442 + y2 = 37.33333333 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333y + y2 = 37.33333333 + 0.4444444442 Combine like terms: 37.33333333 + 0.4444444442 = 37.7777777742 0.4444444442 + 1.333333333y + y2 = 37.7777777742 Factor a perfect square on the left side: (y + 0.6666666665)(y + 0.6666666665) = 37.7777777742 Calculate the square root of the right side: 6.146362971 Break this problem into two subproblems by setting (y + 0.6666666665) equal to 6.146362971 and -6.146362971.

Subproblem 1

y + 0.6666666665 = 6.146362971 Simplifying y + 0.6666666665 = 6.146362971 Reorder the terms: 0.6666666665 + y = 6.146362971 Solving 0.6666666665 + y = 6.146362971 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + y = 6.146362971 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = 6.146362971 + -0.6666666665 y = 6.146362971 + -0.6666666665 Combine like terms: 6.146362971 + -0.6666666665 = 5.4796963045 y = 5.4796963045 Simplifying y = 5.4796963045

Subproblem 2

y + 0.6666666665 = -6.146362971 Simplifying y + 0.6666666665 = -6.146362971 Reorder the terms: 0.6666666665 + y = -6.146362971 Solving 0.6666666665 + y = -6.146362971 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + y = -6.146362971 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = -6.146362971 + -0.6666666665 y = -6.146362971 + -0.6666666665 Combine like terms: -6.146362971 + -0.6666666665 = -6.8130296375 y = -6.8130296375 Simplifying y = -6.8130296375

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.4796963045, -6.8130296375}

Solution

y = {5.4796963045, -6.8130296375}

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