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Simplifying (7r2 + -6r)(2r + -4) = 0 Reorder the terms: (-6r + 7r2)(2r + -4) = 0 Reorder the terms: (-6r + 7r2)(-4 + 2r) = 0 Multiply (-6r + 7r2) * (-4 + 2r) (-6r * (-4 + 2r) + 7r2 * (-4 + 2r)) = 0 ((-4 * -6r + 2r * -6r) + 7r2 * (-4 + 2r)) = 0 ((24r + -12r2) + 7r2 * (-4 + 2r)) = 0 (24r + -12r2 + (-4 * 7r2 + 2r * 7r2)) = 0 (24r + -12r2 + (-28r2 + 14r3)) = 0 Combine like terms: -12r2 + -28r2 = -40r2 (24r + -40r2 + 14r3) = 0 Solving 24r + -40r2 + 14r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(12 + -20r + 7r2) = 0 Factor a trinomial. 2r((6 + -7r)(2 + -1r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(6 + -7r)' equal to zero and attempt to solve: Simplifying 6 + -7r = 0 Solving 6 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7r = 0 + -6 -7r = 0 + -6 Combine like terms: 0 + -6 = -6 -7r = -6 Divide each side by '-7'. r = 0.8571428571 Simplifying r = 0.8571428571Subproblem 3
Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2Solution
r = {0, 0.8571428571, 2}
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