5r^2+7r-43=9

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Solution for 5r^2+7r-43=9 equation:


Simplifying
5r2 + 7r + -43 = 9

Reorder the terms:
-43 + 7r + 5r2 = 9

Solving
-43 + 7r + 5r2 = 9

Solving for variable 'r'.

Reorder the terms:
-43 + -9 + 7r + 5r2 = 9 + -9

Combine like terms: -43 + -9 = -52
-52 + 7r + 5r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-52 + 7r + 5r2 = 0

Factor a trinomial.
(-4 + -1r)(13 + -5r) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(13 + -5r)' equal to zero and attempt to solve: Simplifying 13 + -5r = 0 Solving 13 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -5r = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -5r = 0 + -13 -5r = 0 + -13 Combine like terms: 0 + -13 = -13 -5r = -13 Divide each side by '-5'. r = 2.6 Simplifying r = 2.6

Solution

r = {-4, 2.6}

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