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Simplifying (4r + -3)(3r + 4) = 0 Reorder the terms: (-3 + 4r)(3r + 4) = 0 Reorder the terms: (-3 + 4r)(4 + 3r) = 0 Multiply (-3 + 4r) * (4 + 3r) (-3(4 + 3r) + 4r * (4 + 3r)) = 0 ((4 * -3 + 3r * -3) + 4r * (4 + 3r)) = 0 ((-12 + -9r) + 4r * (4 + 3r)) = 0 (-12 + -9r + (4 * 4r + 3r * 4r)) = 0 (-12 + -9r + (16r + 12r2)) = 0 Combine like terms: -9r + 16r = 7r (-12 + 7r + 12r2) = 0 Solving -12 + 7r + 12r2 = 0 Solving for variable 'r'. Factor a trinomial. (-4 + -3r)(3 + -4r) = 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 + -4r)' equal to zero and attempt to solve: Simplifying 3 + -4r = 0 Solving 3 + -4r = 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 + -4r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4r = 0 + -3 -4r = 0 + -3 Combine like terms: 0 + -3 = -3 -4r = -3 Divide each side by '-4'. r = 0.75 Simplifying r = 0.75Solution
r = {-1.333333333, 0.75}
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