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Simplifying (5r + 2)(3r + -4) = 0 Reorder the terms: (2 + 5r)(3r + -4) = 0 Reorder the terms: (2 + 5r)(-4 + 3r) = 0 Multiply (2 + 5r) * (-4 + 3r) (2(-4 + 3r) + 5r * (-4 + 3r)) = 0 ((-4 * 2 + 3r * 2) + 5r * (-4 + 3r)) = 0 ((-8 + 6r) + 5r * (-4 + 3r)) = 0 (-8 + 6r + (-4 * 5r + 3r * 5r)) = 0 (-8 + 6r + (-20r + 15r2)) = 0 Combine like terms: 6r + -20r = -14r (-8 + -14r + 15r2) = 0 Solving -8 + -14r + 15r2 = 0 Solving for variable 'r'. Factor a trinomial. (-2 + -5r)(4 + -3r) = 0Subproblem 1
Set the factor '(-2 + -5r)' equal to zero and attempt to solve: Simplifying -2 + -5r = 0 Solving -2 + -5r = 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 + -5r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5r = 0 + 2 -5r = 0 + 2 Combine like terms: 0 + 2 = 2 -5r = 2 Divide each side by '-5'. r = -0.4 Simplifying r = -0.4Subproblem 2
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 = 1.333333333Solution
r = {-0.4, 1.333333333}
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