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Simplifying (4r + 3)(r + -12) = 0 Reorder the terms: (3 + 4r)(r + -12) = 0 Reorder the terms: (3 + 4r)(-12 + r) = 0 Multiply (3 + 4r) * (-12 + r) (3(-12 + r) + 4r * (-12 + r)) = 0 ((-12 * 3 + r * 3) + 4r * (-12 + r)) = 0 ((-36 + 3r) + 4r * (-12 + r)) = 0 (-36 + 3r + (-12 * 4r + r * 4r)) = 0 (-36 + 3r + (-48r + 4r2)) = 0 Combine like terms: 3r + -48r = -45r (-36 + -45r + 4r2) = 0 Solving -36 + -45r + 4r2 = 0 Solving for variable 'r'. Factor a trinomial. (-3 + -4r)(12 + -1r) = 0Subproblem 1
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 = -0.75Subproblem 2
Set the factor '(12 + -1r)' equal to zero and attempt to solve: Simplifying 12 + -1r = 0 Solving 12 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1r = 0 + -12 -1r = 0 + -12 Combine like terms: 0 + -12 = -12 -1r = -12 Divide each side by '-1'. r = 12 Simplifying r = 12Solution
r = {-0.75, 12}
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