9r^2+16r=-7r^2-4

Solution for 9r^2+16r=-7r^2-4 equation:

Simplifying
9r2 + 16r = -7r2 + -4

Reorder the terms:
16r + 9r2 = -7r2 + -4

Reorder the terms:
16r + 9r2 = -4 + -7r2

Solving
16r + 9r2 = -4 + -7r2

Solving for variable 'r'.

Reorder the terms:
4 + 16r + 9r2 + 7r2 = -4 + -7r2 + 4 + 7r2

Combine like terms: 9r2 + 7r2 = 16r2
4 + 16r + 16r2 = -4 + -7r2 + 4 + 7r2

Reorder the terms:
4 + 16r + 16r2 = -4 + 4 + -7r2 + 7r2

Combine like terms: -4 + 4 = 0
4 + 16r + 16r2 = 0 + -7r2 + 7r2
4 + 16r + 16r2 = -7r2 + 7r2

Combine like terms: -7r2 + 7r2 = 0
4 + 16r + 16r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 4r + 4r2) = 0

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

Ignore the factor 4.
Subproblem 1
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
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 = {-0.5, -0.5}