2(r+5)=10-4r^2

Solution for 2(r+5)=10-4r^2 equation:

Simplifying
2(r + 5) = 10 + -4r2

Reorder the terms:
2(5 + r) = 10 + -4r2
(5 * 2 + r * 2) = 10 + -4r2
(10 + 2r) = 10 + -4r2

Add '-10' to each side of the equation.
10 + -10 + 2r = 10 + -10 + -4r2

Combine like terms: 10 + -10 = 0
0 + 2r = 10 + -10 + -4r2
2r = 10 + -10 + -4r2

Combine like terms: 10 + -10 = 0
2r = 0 + -4r2
2r = -4r2

Solving
2r = -4r2

Solving for variable 'r'.

Combine like terms: -4r2 + 4r2 = 0
2r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2r'.
2r(1 + 2r) = 0

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

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(1 + 2r)' equal to zero and attempt to solve:

Simplifying
1 + 2r = 0

Solving
1 + 2r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2r = 0 + -1
2r = 0 + -1

Combine like terms: 0 + -1 = -1
2r = -1

Divide each side by '2'.
r = -0.5

Simplifying
r = -0.5
Solution
r = {0, -0.5}