-4r^2+5r+6=2-5r^2

Solution for -4r^2+5r+6=2-5r^2 equation:

Simplifying
-4r2 + 5r + 6 = 2 + -5r2

Reorder the terms:
6 + 5r + -4r2 = 2 + -5r2

Solving
6 + 5r + -4r2 = 2 + -5r2

Solving for variable 'r'.

Reorder the terms:
6 + -2 + 5r + -4r2 + 5r2 = 2 + -5r2 + -2 + 5r2

Combine like terms: 6 + -2 = 4
4 + 5r + -4r2 + 5r2 = 2 + -5r2 + -2 + 5r2

Combine like terms: -4r2 + 5r2 = 1r2
4 + 5r + 1r2 = 2 + -5r2 + -2 + 5r2

Reorder the terms:
4 + 5r + 1r2 = 2 + -2 + -5r2 + 5r2

Combine like terms: 2 + -2 = 0
4 + 5r + 1r2 = 0 + -5r2 + 5r2
4 + 5r + 1r2 = -5r2 + 5r2

Combine like terms: -5r2 + 5r2 = 0
4 + 5r + 1r2 = 0

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

Subproblem 1
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

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

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

Simplifying
r = -4
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 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 + r = 0 + -1

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

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

Simplifying
r = -1
Solution
r = {-4, -1}