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Simplifying 0 = 0 + -2y3(2y2 + -5y + 6) Reorder the terms: 0 = 0 + -2y3(6 + -5y + 2y2) 0 = 0 + (6 * -2y3 + -5y * -2y3 + 2y2 * -2y3) 0 = 0 + (-12y3 + 10y4 + -4y5) Remove the zero: 0 = -12y3 + 10y4 + -4y5 Solving 0 = -12y3 + 10y4 + -4y5 Solving for variable 'y'. Remove the zero: 12y3 + -10y4 + 4y5 = -12y3 + 10y4 + -4y5 + 12y3 + -10y4 + 4y5 Reorder the terms: 12y3 + -10y4 + 4y5 = -12y3 + 12y3 + 10y4 + -10y4 + -4y5 + 4y5 Combine like terms: -12y3 + 12y3 = 0 12y3 + -10y4 + 4y5 = 0 + 10y4 + -10y4 + -4y5 + 4y5 12y3 + -10y4 + 4y5 = 10y4 + -10y4 + -4y5 + 4y5 Combine like terms: 10y4 + -10y4 = 0 12y3 + -10y4 + 4y5 = 0 + -4y5 + 4y5 12y3 + -10y4 + 4y5 = -4y5 + 4y5 Combine like terms: -4y5 + 4y5 = 0 12y3 + -10y4 + 4y5 = 0 Factor out the Greatest Common Factor (GCF), '2y3'. 2y3(6 + -5y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve: Simplifying y3 = 0 Solving y3 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(6 + -5y + 2y2)' equal to zero and attempt to solve: Simplifying 6 + -5y + 2y2 = 0 Solving 6 + -5y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -2.5y + y2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2.5y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + -2.5y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2.5y + y2 = 0 + -3 -2.5y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2.5y + y2 = -3 The y term is -2.5y. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5y + 1.5625 + y2 = -3 + 1.5625 Reorder the terms: 1.5625 + -2.5y + y2 = -3 + 1.5625 Combine like terms: -3 + 1.5625 = -1.4375 1.5625 + -2.5y + y2 = -1.4375 Factor a perfect square on the left side: (y + -1.25)(y + -1.25) = -1.4375 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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