4r^2+12r-35=5

Solution for 4r^2+12r-35=5 equation:

Simplifying
4r2 + 12r + -35 = 5

Reorder the terms:
-35 + 12r + 4r2 = 5

Solving
-35 + 12r + 4r2 = 5

Solving for variable 'r'.

Reorder the terms:
-35 + -5 + 12r + 4r2 = 5 + -5

Combine like terms: -35 + -5 = -40
-40 + 12r + 4r2 = 5 + -5

Combine like terms: 5 + -5 = 0
-40 + 12r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 3r + r2) = 0

Factor a trinomial.
4((-5 + -1r)(2 + -1r)) = 0

Ignore the factor 4.
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}