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Simplifying 3(6r + -3)(6r + -3) = 10(6r + -3) + 25 Reorder the terms: 3(-3 + 6r)(6r + -3) = 10(6r + -3) + 25 Reorder the terms: 3(-3 + 6r)(-3 + 6r) = 10(6r + -3) + 25 Multiply (-3 + 6r) * (-3 + 6r) 3(-3(-3 + 6r) + 6r * (-3 + 6r)) = 10(6r + -3) + 25 3((-3 * -3 + 6r * -3) + 6r * (-3 + 6r)) = 10(6r + -3) + 25 3((9 + -18r) + 6r * (-3 + 6r)) = 10(6r + -3) + 25 3(9 + -18r + (-3 * 6r + 6r * 6r)) = 10(6r + -3) + 25 3(9 + -18r + (-18r + 36r2)) = 10(6r + -3) + 25 Combine like terms: -18r + -18r = -36r 3(9 + -36r + 36r2) = 10(6r + -3) + 25 (9 * 3 + -36r * 3 + 36r2 * 3) = 10(6r + -3) + 25 (27 + -108r + 108r2) = 10(6r + -3) + 25 Reorder the terms: 27 + -108r + 108r2 = 10(-3 + 6r) + 25 27 + -108r + 108r2 = (-3 * 10 + 6r * 10) + 25 27 + -108r + 108r2 = (-30 + 60r) + 25 Reorder the terms: 27 + -108r + 108r2 = -30 + 25 + 60r Combine like terms: -30 + 25 = -5 27 + -108r + 108r2 = -5 + 60r Solving 27 + -108r + 108r2 = -5 + 60r Solving for variable 'r'. Reorder the terms: 27 + 5 + -108r + -60r + 108r2 = -5 + 60r + 5 + -60r Combine like terms: 27 + 5 = 32 32 + -108r + -60r + 108r2 = -5 + 60r + 5 + -60r Combine like terms: -108r + -60r = -168r 32 + -168r + 108r2 = -5 + 60r + 5 + -60r Reorder the terms: 32 + -168r + 108r2 = -5 + 5 + 60r + -60r Combine like terms: -5 + 5 = 0 32 + -168r + 108r2 = 0 + 60r + -60r 32 + -168r + 108r2 = 60r + -60r Combine like terms: 60r + -60r = 0 32 + -168r + 108r2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(8 + -42r + 27r2) = 0 Factor a trinomial. 4((2 + -9r)(4 + -3r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -9r)' equal to zero and attempt to solve: Simplifying 2 + -9r = 0 Solving 2 + -9r = 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 + -9r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9r = 0 + -2 -9r = 0 + -2 Combine like terms: 0 + -2 = -2 -9r = -2 Divide each side by '-9'. r = 0.2222222222 Simplifying r = 0.2222222222Subproblem 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 = {0.2222222222, 1.333333333}
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