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Simplifying 8(y + -1) * 3y = 6(2y + -6) Reorder the terms: 8(-1 + y) * 3y = 6(2y + -6) Reorder the terms for easier multiplication: 8 * 3y(-1 + y) = 6(2y + -6) Multiply 8 * 3 24y(-1 + y) = 6(2y + -6) (-1 * 24y + y * 24y) = 6(2y + -6) (-24y + 24y2) = 6(2y + -6) Reorder the terms: -24y + 24y2 = 6(-6 + 2y) -24y + 24y2 = (-6 * 6 + 2y * 6) -24y + 24y2 = (-36 + 12y) Solving -24y + 24y2 = -36 + 12y Solving for variable 'y'. Reorder the terms: 36 + -24y + -12y + 24y2 = -36 + 12y + 36 + -12y Combine like terms: -24y + -12y = -36y 36 + -36y + 24y2 = -36 + 12y + 36 + -12y Reorder the terms: 36 + -36y + 24y2 = -36 + 36 + 12y + -12y Combine like terms: -36 + 36 = 0 36 + -36y + 24y2 = 0 + 12y + -12y 36 + -36y + 24y2 = 12y + -12y Combine like terms: 12y + -12y = 0 36 + -36y + 24y2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(3 + -3y + 2y2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(3 + -3y + 2y2)' equal to zero and attempt to solve: Simplifying 3 + -3y + 2y2 = 0 Solving 3 + -3y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -1.5y + y2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -1.5y + -1.5 + y2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -1.5y + y2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -1.5y + y2 = 0 + -1.5 -1.5y + y2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -1.5y + y2 = -1.5 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = -1.5 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = -1.5 + 0.5625 Combine like terms: -1.5 + 0.5625 = -0.9375 0.5625 + -1.5y + y2 = -0.9375 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = -0.9375 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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