r(r+3)=10

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Solution for r(r+3)=10 equation:


Simplifying
r(r + 3) = 10

Reorder the terms:
r(3 + r) = 10
(3 * r + r * r) = 10
(3r + r2) = 10

Solving
3r + r2 = 10

Solving for variable 'r'.

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

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

Factor a trinomial.
(-5 + -1r)(2 + -1r) = 0

Subproblem 1

Set the factor '(-5 + -1r)' equal to zero and attempt to solve: Simplifying -5 + -1r = 0 Solving -5 + -1r = 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 + -1r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1r = 0 + 5 -1r = 0 + 5 Combine like terms: 0 + 5 = 5 -1r = 5 Divide each side by '-1'. r = -5 Simplifying r = -5

Subproblem 2

Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2

Solution

r = {-5, 2}

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