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Simplifying (-2m + -5)(3m + 6) = (6m + -5)(m + -4) Reorder the terms: (-5 + -2m)(3m + 6) = (6m + -5)(m + -4) Reorder the terms: (-5 + -2m)(6 + 3m) = (6m + -5)(m + -4) Multiply (-5 + -2m) * (6 + 3m) (-5(6 + 3m) + -2m * (6 + 3m)) = (6m + -5)(m + -4) ((6 * -5 + 3m * -5) + -2m * (6 + 3m)) = (6m + -5)(m + -4) ((-30 + -15m) + -2m * (6 + 3m)) = (6m + -5)(m + -4) (-30 + -15m + (6 * -2m + 3m * -2m)) = (6m + -5)(m + -4) (-30 + -15m + (-12m + -6m2)) = (6m + -5)(m + -4) Combine like terms: -15m + -12m = -27m (-30 + -27m + -6m2) = (6m + -5)(m + -4) Reorder the terms: -30 + -27m + -6m2 = (-5 + 6m)(m + -4) Reorder the terms: -30 + -27m + -6m2 = (-5 + 6m)(-4 + m) Multiply (-5 + 6m) * (-4 + m) -30 + -27m + -6m2 = (-5(-4 + m) + 6m * (-4 + m)) -30 + -27m + -6m2 = ((-4 * -5 + m * -5) + 6m * (-4 + m)) -30 + -27m + -6m2 = ((20 + -5m) + 6m * (-4 + m)) -30 + -27m + -6m2 = (20 + -5m + (-4 * 6m + m * 6m)) -30 + -27m + -6m2 = (20 + -5m + (-24m + 6m2)) Combine like terms: -5m + -24m = -29m -30 + -27m + -6m2 = (20 + -29m + 6m2) Solving -30 + -27m + -6m2 = 20 + -29m + 6m2 Solving for variable 'm'. Reorder the terms: -30 + -20 + -27m + 29m + -6m2 + -6m2 = 20 + -29m + 6m2 + -20 + 29m + -6m2 Combine like terms: -30 + -20 = -50 -50 + -27m + 29m + -6m2 + -6m2 = 20 + -29m + 6m2 + -20 + 29m + -6m2 Combine like terms: -27m + 29m = 2m -50 + 2m + -6m2 + -6m2 = 20 + -29m + 6m2 + -20 + 29m + -6m2 Combine like terms: -6m2 + -6m2 = -12m2 -50 + 2m + -12m2 = 20 + -29m + 6m2 + -20 + 29m + -6m2 Reorder the terms: -50 + 2m + -12m2 = 20 + -20 + -29m + 29m + 6m2 + -6m2 Combine like terms: 20 + -20 = 0 -50 + 2m + -12m2 = 0 + -29m + 29m + 6m2 + -6m2 -50 + 2m + -12m2 = -29m + 29m + 6m2 + -6m2 Combine like terms: -29m + 29m = 0 -50 + 2m + -12m2 = 0 + 6m2 + -6m2 -50 + 2m + -12m2 = 6m2 + -6m2 Combine like terms: 6m2 + -6m2 = 0 -50 + 2m + -12m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + m + -6m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + m + -6m2)' equal to zero and attempt to solve: Simplifying -25 + m + -6m2 = 0 Solving -25 + m + -6m2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 4.166666667 + -0.1666666667m + m2 = 0 Move the constant term to the right: Add '-4.166666667' to each side of the equation. 4.166666667 + -0.1666666667m + -4.166666667 + m2 = 0 + -4.166666667 Reorder the terms: 4.166666667 + -4.166666667 + -0.1666666667m + m2 = 0 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + -0.1666666667m + m2 = 0 + -4.166666667 -0.1666666667m + m2 = 0 + -4.166666667 Combine like terms: 0 + -4.166666667 = -4.166666667 -0.1666666667m + m2 = -4.166666667 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1666666667m + 0.25 + m2 = -4.166666667 + 0.25 Reorder the terms: 0.25 + -0.1666666667m + m2 = -4.166666667 + 0.25 Combine like terms: -4.166666667 + 0.25 = -3.916666667 0.25 + -0.1666666667m + m2 = -3.916666667 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = -3.916666667 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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