18r^2+33r-105=0

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Solution for 18r^2+33r-105=0 equation:


Simplifying
18r2 + 33r + -105 = 0

Reorder the terms:
-105 + 33r + 18r2 = 0

Solving
-105 + 33r + 18r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + 11r + 6r2) = 0

Factor a trinomial.
3((-7 + -2r)(5 + -3r)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-7 + -2r)' equal to zero and attempt to solve: Simplifying -7 + -2r = 0 Solving -7 + -2r = 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 + -2r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2r = 0 + 7 -2r = 0 + 7 Combine like terms: 0 + 7 = 7 -2r = 7 Divide each side by '-2'. r = -3.5 Simplifying r = -3.5

Subproblem 2

Set the factor '(5 + -3r)' equal to zero and attempt to solve: Simplifying 5 + -3r = 0 Solving 5 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3r = 0 + -5 -3r = 0 + -5 Combine like terms: 0 + -5 = -5 -3r = -5 Divide each side by '-3'. r = 1.666666667 Simplifying r = 1.666666667

Solution

r = {-3.5, 1.666666667}

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