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Simplifying -2y(3y2 + -7y + -12) = 0 Reorder the terms: -2y(-12 + -7y + 3y2) = 0 (-12 * -2y + -7y * -2y + 3y2 * -2y) = 0 (24y + 14y2 + -6y3) = 0 Solving 24y + 14y2 + -6y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(12 + 7y + -3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(12 + 7y + -3y2)' equal to zero and attempt to solve: Simplifying 12 + 7y + -3y2 = 0 Solving 12 + 7y + -3y2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4 + -2.333333333y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.333333333y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -2.333333333y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.333333333y + y2 = 0 + 4 -2.333333333y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.333333333y + y2 = 4 The y term is -2.333333333y. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333y + 1.361111112 + y2 = 4 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333y + y2 = 4 + 1.361111112 Combine like terms: 4 + 1.361111112 = 5.361111112 1.361111112 + -2.333333333y + y2 = 5.361111112 Factor a perfect square on the left side: (y + -1.166666667)(y + -1.166666667) = 5.361111112 Calculate the square root of the right side: 2.315407332 Break this problem into two subproblems by setting (y + -1.166666667) equal to 2.315407332 and -2.315407332.Subproblem 1
y + -1.166666667 = 2.315407332 Simplifying y + -1.166666667 = 2.315407332 Reorder the terms: -1.166666667 + y = 2.315407332 Solving -1.166666667 + y = 2.315407332 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = 2.315407332 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = 2.315407332 + 1.166666667 y = 2.315407332 + 1.166666667 Combine like terms: 2.315407332 + 1.166666667 = 3.482073999 y = 3.482073999 Simplifying y = 3.482073999Subproblem 2
y + -1.166666667 = -2.315407332 Simplifying y + -1.166666667 = -2.315407332 Reorder the terms: -1.166666667 + y = -2.315407332 Solving -1.166666667 + y = -2.315407332 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = -2.315407332 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = -2.315407332 + 1.166666667 y = -2.315407332 + 1.166666667 Combine like terms: -2.315407332 + 1.166666667 = -1.148740665 y = -1.148740665 Simplifying y = -1.148740665Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.482073999, -1.148740665}Solution
y = {0, 3.482073999, -1.148740665}
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