6r^2-10r=24

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Solution for 6r^2-10r=24 equation:


Simplifying
6r2 + -10r = 24

Reorder the terms:
-10r + 6r2 = 24

Solving
-10r + 6r2 = 24

Solving for variable 'r'.

Reorder the terms:
-24 + -10r + 6r2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -10r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -5r + 3r2) = 0

Factor a trinomial.
2((-4 + -3r)(3 + -1r)) = 0

Ignore the factor 2.

Subproblem 1

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 = -1.333333333

Subproblem 2

Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3

Solution

r = {-1.333333333, 3}

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