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Simplifying (2r + 3)(r + -2) = 0 Reorder the terms: (3 + 2r)(r + -2) = 0 Reorder the terms: (3 + 2r)(-2 + r) = 0 Multiply (3 + 2r) * (-2 + r) (3(-2 + r) + 2r * (-2 + r)) = 0 ((-2 * 3 + r * 3) + 2r * (-2 + r)) = 0 ((-6 + 3r) + 2r * (-2 + r)) = 0 (-6 + 3r + (-2 * 2r + r * 2r)) = 0 (-6 + 3r + (-4r + 2r2)) = 0 Combine like terms: 3r + -4r = -1r (-6 + -1r + 2r2) = 0 Solving -6 + -1r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (-3 + -2r)(2 + -1r) = 0Subproblem 1
Set the factor '(-3 + -2r)' equal to zero and attempt to solve: Simplifying -3 + -2r = 0 Solving -3 + -2r = 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 + -2r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2r = 0 + 3 -2r = 0 + 3 Combine like terms: 0 + 3 = 3 -2r = 3 Divide each side by '-2'. r = -1.5 Simplifying r = -1.5Subproblem 2
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 = {-1.5, 2}
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