3r^2+10r-4=84

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Solution for 3r^2+10r-4=84 equation:


Simplifying
3r2 + 10r + -4 = 84

Reorder the terms:
-4 + 10r + 3r2 = 84

Solving
-4 + 10r + 3r2 = 84

Solving for variable 'r'.

Reorder the terms:
-4 + -84 + 10r + 3r2 = 84 + -84

Combine like terms: -4 + -84 = -88
-88 + 10r + 3r2 = 84 + -84

Combine like terms: 84 + -84 = 0
-88 + 10r + 3r2 = 0

Factor a trinomial.
(-22 + -3r)(4 + -1r) = 0

Subproblem 1

Set the factor '(-22 + -3r)' equal to zero and attempt to solve: Simplifying -22 + -3r = 0 Solving -22 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + -3r = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -3r = 0 + 22 -3r = 0 + 22 Combine like terms: 0 + 22 = 22 -3r = 22 Divide each side by '-3'. r = -7.333333333 Simplifying r = -7.333333333

Subproblem 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 = 4

Solution

r = {-7.333333333, 4}

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