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Simplifying 4y(3 + -2y) + -5(3y + 2) = 0 (3 * 4y + -2y * 4y) + -5(3y + 2) = 0 (12y + -8y2) + -5(3y + 2) = 0 Reorder the terms: 12y + -8y2 + -5(2 + 3y) = 0 12y + -8y2 + (2 * -5 + 3y * -5) = 0 12y + -8y2 + (-10 + -15y) = 0 Reorder the terms: -10 + 12y + -15y + -8y2 = 0 Combine like terms: 12y + -15y = -3y -10 + -3y + -8y2 = 0 Solving -10 + -3y + -8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 3y + 8y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 3y + 8y2)' equal to zero and attempt to solve: Simplifying 10 + 3y + 8y2 = 0 Solving 10 + 3y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.25 + 0.375y + y2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.375y + -1.25 + y2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.375y + y2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.375y + y2 = 0 + -1.25 0.375y + y2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.375y + y2 = -1.25 The y term is 0.375y. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375y + 0.03515625 + y2 = -1.25 + 0.03515625 Reorder the terms: 0.03515625 + 0.375y + y2 = -1.25 + 0.03515625 Combine like terms: -1.25 + 0.03515625 = -1.21484375 0.03515625 + 0.375y + y2 = -1.21484375 Factor a perfect square on the left side: (y + 0.1875)(y + 0.1875) = -1.21484375 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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