2r^2+24r+70=0

Solution for 2r^2+24r+70=0 equation:

Simplifying
2r2 + 24r + 70 = 0

Reorder the terms:
70 + 24r + 2r2 = 0

Solving
70 + 24r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + 12r + r2) = 0

Factor a trinomial.
2((7 + r)(5 + r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + r)' equal to zero and attempt to solve:

Simplifying
7 + r = 0

Solving
7 + r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + r = 0 + -7
r = 0 + -7

Combine like terms: 0 + -7 = -7
r = -7

Simplifying
r = -7
Subproblem 2
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 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 + r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + r = 0 + -5
r = 0 + -5

Combine like terms: 0 + -5 = -5
r = -5

Simplifying
r = -5
Solution
r = {-7, -5}