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Simplifying 2(u + -1) * 3u = 3(u + -6) Reorder the terms: 2(-1 + u) * 3u = 3(u + -6) Reorder the terms for easier multiplication: 2 * 3u(-1 + u) = 3(u + -6) Multiply 2 * 3 6u(-1 + u) = 3(u + -6) (-1 * 6u + u * 6u) = 3(u + -6) (-6u + 6u2) = 3(u + -6) Reorder the terms: -6u + 6u2 = 3(-6 + u) -6u + 6u2 = (-6 * 3 + u * 3) -6u + 6u2 = (-18 + 3u) Solving -6u + 6u2 = -18 + 3u Solving for variable 'u'. Reorder the terms: 18 + -6u + -3u + 6u2 = -18 + 3u + 18 + -3u Combine like terms: -6u + -3u = -9u 18 + -9u + 6u2 = -18 + 3u + 18 + -3u Reorder the terms: 18 + -9u + 6u2 = -18 + 18 + 3u + -3u Combine like terms: -18 + 18 = 0 18 + -9u + 6u2 = 0 + 3u + -3u 18 + -9u + 6u2 = 3u + -3u Combine like terms: 3u + -3u = 0 18 + -9u + 6u2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -3u + 2u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -3u + 2u2)' equal to zero and attempt to solve: Simplifying 6 + -3u + 2u2 = 0 Solving 6 + -3u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -1.5u + u2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -1.5u + -3 + u2 = 0 + -3 Reorder the terms: 3 + -3 + -1.5u + u2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1.5u + u2 = 0 + -3 -1.5u + u2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1.5u + u2 = -3 The u term is -1.5u. 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. -1.5u + 0.5625 + u2 = -3 + 0.5625 Reorder the terms: 0.5625 + -1.5u + u2 = -3 + 0.5625 Combine like terms: -3 + 0.5625 = -2.4375 0.5625 + -1.5u + u2 = -2.4375 Factor a perfect square on the left side: (u + -0.75)(u + -0.75) = -2.4375 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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