20r^2-r=30

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Solution for 20r^2-r=30 equation:


Simplifying
20r2 + -1r = 30

Reorder the terms:
-1r + 20r2 = 30

Solving
-1r + 20r2 = 30

Solving for variable 'r'.

Reorder the terms:
-30 + -1r + 20r2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -1r + 20r2 = 0

Factor a trinomial.
(-6 + -5r)(5 + -4r) = 0

Subproblem 1

Set the factor '(-6 + -5r)' equal to zero and attempt to solve: Simplifying -6 + -5r = 0 Solving -6 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5r = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5r = 0 + 6 -5r = 0 + 6 Combine like terms: 0 + 6 = 6 -5r = 6 Divide each side by '-5'. r = -1.2 Simplifying r = -1.2

Subproblem 2

Set the factor '(5 + -4r)' equal to zero and attempt to solve: Simplifying 5 + -4r = 0 Solving 5 + -4r = 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 + -4r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4r = 0 + -5 -4r = 0 + -5 Combine like terms: 0 + -5 = -5 -4r = -5 Divide each side by '-4'. r = 1.25 Simplifying r = 1.25

Solution

r = {-1.2, 1.25}

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