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Following the general rule in solving algebraic expressions, it is assumed that we will be finding the value of the variable “R” in the problem.
First, we should simplify the equation:
2r2 + 11r + 15 = 0
Reorder the terms:
15 + 11r + 2r2 = 0
15 + 11r + 2r2 = 0
Solving for variable 'r'.
Factor a trinomial.
(3 + r)(5 + 2r) = 0
Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve:
Simplifying
3 + r = 0
Solving
3 + r = 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 + r = 0 + -3
Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3
Combine like terms: 0 + -3 = -3
r = -3
Simplifying
r = -3
Subproblem 2
Set the factor '(5 + 2r)' equal to zero and attempt to solve:
Simplifying
5 + 2r = 0
Solving
5 + 2r = 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 + 2r = 0 + -5
Combine like terms: 5 + -5 = 0
0 + 2r = 0 + -5
2r = 0 + -5
Combine like terms: 0 + -5 = -5
2r = -5
Divide each side by '2'.
r = -2.5
Simplifying
r = -2.5
Solution
r = {-3, -2.5}