r^2+4r-5=7

Solution for r^2+4r-5=7 equation:

Simplifying
r2 + 4r + -5 = 7

Reorder the terms:
-5 + 4r + r2 = 7

Solving
-5 + 4r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
-5 + -7 + 4r + r2 = 7 + -7

Combine like terms: -5 + -7 = -12
-12 + 4r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-12 + 4r + r2 = 0

Factor a trinomial.
(-6 + -1r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 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 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
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 = {-6, 2}