r^2+2r-5=3

Solution for r^2+2r-5=3 equation:

Simplifying
r2 + 2r + -5 = 3

Reorder the terms:
-5 + 2r + r2 = 3

Solving
-5 + 2r + r2 = 3

Solving for variable 'r'.

Reorder the terms:
-5 + -3 + 2r + r2 = 3 + -3

Combine like terms: -5 + -3 = -8
-8 + 2r + r2 = 3 + -3

Combine like terms: 3 + -3 = 0
-8 + 2r + r2 = 0

Factor a trinomial.
(-4 + -1r)(2 + -1r) = 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 '(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 = {-4, 2}