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Simplifying 7r3 + 42r2 = 49r Reorder the terms: 42r2 + 7r3 = 49r Solving 42r2 + 7r3 = 49r Solving for variable 'r'. Reorder the terms: -49r + 42r2 + 7r3 = 49r + -49r Combine like terms: 49r + -49r = 0 -49r + 42r2 + 7r3 = 0 Factor out the Greatest Common Factor (GCF), '7r'. 7r(-7 + 6r + r2) = 0 Factor a trinomial. 7r((-7 + -1r)(1 + -1r)) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(-7 + -1r)' equal to zero and attempt to solve: Simplifying -7 + -1r = 0 Solving -7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1r = 0 + 7 -1r = 0 + 7 Combine like terms: 0 + 7 = 7 -1r = 7 Divide each side by '-1'. r = -7 Simplifying r = -7Subproblem 3
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 = 1Solution
r = {0, -7, 1}
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