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Simplifying (3r + 4)(r + -3) = 0 Reorder the terms: (4 + 3r)(r + -3) = 0 Reorder the terms: (4 + 3r)(-3 + r) = 0 Multiply (4 + 3r) * (-3 + r) (4(-3 + r) + 3r * (-3 + r)) = 0 ((-3 * 4 + r * 4) + 3r * (-3 + r)) = 0 ((-12 + 4r) + 3r * (-3 + r)) = 0 (-12 + 4r + (-3 * 3r + r * 3r)) = 0 (-12 + 4r + (-9r + 3r2)) = 0 Combine like terms: 4r + -9r = -5r (-12 + -5r + 3r2) = 0 Solving -12 + -5r + 3r2 = 0 Solving for variable 'r'. Factor a trinomial. (-4 + -3r)(3 + -1r) = 0Subproblem 1
Set the factor '(-4 + -3r)' equal to zero and attempt to solve: Simplifying -4 + -3r = 0 Solving -4 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3r = 0 + 4 -3r = 0 + 4 Combine like terms: 0 + 4 = 4 -3r = 4 Divide each side by '-3'. r = -1.333333333 Simplifying r = -1.333333333Subproblem 2
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 = {-1.333333333, 3}
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