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Simplifying 5r(4r + 7)(r + -3) = 0 Reorder the terms: 5r(7 + 4r)(r + -3) = 0 Reorder the terms: 5r(7 + 4r)(-3 + r) = 0 Multiply (7 + 4r) * (-3 + r) 5r(7(-3 + r) + 4r * (-3 + r)) = 0 5r((-3 * 7 + r * 7) + 4r * (-3 + r)) = 0 5r((-21 + 7r) + 4r * (-3 + r)) = 0 5r(-21 + 7r + (-3 * 4r + r * 4r)) = 0 5r(-21 + 7r + (-12r + 4r2)) = 0 Combine like terms: 7r + -12r = -5r 5r(-21 + -5r + 4r2) = 0 (-21 * 5r + -5r * 5r + 4r2 * 5r) = 0 (-105r + -25r2 + 20r3) = 0 Solving -105r + -25r2 + 20r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5r'. 5r(-21 + -5r + 4r2) = 0 Factor a trinomial. 5r((-7 + -4r)(3 + -1r)) = 0 Ignore the factor 5.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 '(-7 + -4r)' equal to zero and attempt to solve: Simplifying -7 + -4r = 0 Solving -7 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4r = 0 + 7 -4r = 0 + 7 Combine like terms: 0 + 7 = 7 -4r = 7 Divide each side by '-4'. r = -1.75 Simplifying r = -1.75Subproblem 3
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {0, -1.75, 3}
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