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Simplifying -3y + 5y(1 + -1y) + 4(y2 + -2y + -3) = 0 -3y + (1 * 5y + -1y * 5y) + 4(y2 + -2y + -3) = 0 -3y + (5y + -5y2) + 4(y2 + -2y + -3) = 0 Reorder the terms: -3y + 5y + -5y2 + 4(-3 + -2y + y2) = 0 -3y + 5y + -5y2 + (-3 * 4 + -2y * 4 + y2 * 4) = 0 -3y + 5y + -5y2 + (-12 + -8y + 4y2) = 0 Reorder the terms: -12 + -3y + 5y + -8y + -5y2 + 4y2 = 0 Combine like terms: -3y + 5y = 2y -12 + 2y + -8y + -5y2 + 4y2 = 0 Combine like terms: 2y + -8y = -6y -12 + -6y + -5y2 + 4y2 = 0 Combine like terms: -5y2 + 4y2 = -1y2 -12 + -6y + -1y2 = 0 Solving -12 + -6y + -1y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 6y + y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 6y + y2)' equal to zero and attempt to solve: Simplifying 12 + 6y + y2 = 0 Solving 12 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 6y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + 6y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 6y + y2 = 0 + -12 6y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 6y + y2 = -12 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -12 + 9 Reorder the terms: 9 + 6y + y2 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + 6y + y2 = -3 Factor a perfect square on the left side: (y + 3)(y + 3) = -3 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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