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Simplifying 7r2 + -21r = 28 Reorder the terms: -21r + 7r2 = 28 Solving -21r + 7r2 = 28 Solving for variable 'r'. Reorder the terms: -28 + -21r + 7r2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -21r + 7r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-4 + -3r + r2) = 0 Factor a trinomial. 7((-1 + -1r)(4 + -1r)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + -1r)' equal to zero and attempt to solve: Simplifying -1 + -1r = 0 Solving -1 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1r = 0 + 1 -1r = 0 + 1 Combine like terms: 0 + 1 = 1 -1r = 1 Divide each side by '-1'. r = -1 Simplifying r = -1Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve: Simplifying 4 + -1r = 0 Solving 4 + -1r = 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 + -1r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1r = 0 + -4 -1r = 0 + -4 Combine like terms: 0 + -4 = -4 -1r = -4 Divide each side by '-1'. r = 4 Simplifying r = 4Solution
r = {-1, 4}
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