-4r^2+5r+3=-3-5r^2

Solution for -4r^2+5r+3=-3-5r^2 equation:

Simplifying
-4r2 + 5r + 3 = -3 + -5r2

Reorder the terms:
3 + 5r + -4r2 = -3 + -5r2

Solving
3 + 5r + -4r2 = -3 + -5r2

Solving for variable 'r'.

Reorder the terms:
3 + 3 + 5r + -4r2 + 5r2 = -3 + -5r2 + 3 + 5r2

Combine like terms: 3 + 3 = 6
6 + 5r + -4r2 + 5r2 = -3 + -5r2 + 3 + 5r2

Combine like terms: -4r2 + 5r2 = 1r2
6 + 5r + 1r2 = -3 + -5r2 + 3 + 5r2

Reorder the terms:
6 + 5r + 1r2 = -3 + 3 + -5r2 + 5r2

Combine like terms: -3 + 3 = 0
6 + 5r + 1r2 = 0 + -5r2 + 5r2
6 + 5r + 1r2 = -5r2 + 5r2

Combine like terms: -5r2 + 5r2 = 0
6 + 5r + 1r2 = 0

Factor a trinomial.
(3 + r)(2 + r) = 0

Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 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 + r = 0 + -2

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

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

Simplifying
r = -2
Solution
r = {-3, -2}