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Simplifying -3m(6m + 4) = 2(4m + 15) Reorder the terms: -3m(4 + 6m) = 2(4m + 15) (4 * -3m + 6m * -3m) = 2(4m + 15) (-12m + -18m2) = 2(4m + 15) Reorder the terms: -12m + -18m2 = 2(15 + 4m) -12m + -18m2 = (15 * 2 + 4m * 2) -12m + -18m2 = (30 + 8m) Solving -12m + -18m2 = 30 + 8m Solving for variable 'm'. Reorder the terms: -30 + -12m + -8m + -18m2 = 30 + 8m + -30 + -8m Combine like terms: -12m + -8m = -20m -30 + -20m + -18m2 = 30 + 8m + -30 + -8m Reorder the terms: -30 + -20m + -18m2 = 30 + -30 + 8m + -8m Combine like terms: 30 + -30 = 0 -30 + -20m + -18m2 = 0 + 8m + -8m -30 + -20m + -18m2 = 8m + -8m Combine like terms: 8m + -8m = 0 -30 + -20m + -18m2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(15 + 10m + 9m2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(15 + 10m + 9m2)' equal to zero and attempt to solve: Simplifying 15 + 10m + 9m2 = 0 Solving 15 + 10m + 9m2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.666666667 + 1.111111111m + m2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 1.111111111m + -1.666666667 + m2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 1.111111111m + m2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 1.111111111m + m2 = 0 + -1.666666667 1.111111111m + m2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 1.111111111m + m2 = -1.666666667 The m term is 1.111111111m. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111m + 0.3086419752 + m2 = -1.666666667 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111m + m2 = -1.666666667 + 0.3086419752 Combine like terms: -1.666666667 + 0.3086419752 = -1.3580246918 0.3086419752 + 1.111111111m + m2 = -1.3580246918 Factor a perfect square on the left side: (m + 0.5555555555)(m + 0.5555555555) = -1.3580246918 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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