-5r^2-3r-15=4r-7-6r^2

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Solution for -5r^2-3r-15=4r-7-6r^2 equation: 


Simplifying
-5r2 + -3r + -15 = 4r + -7 + -6r2

Reorder the terms:
-15 + -3r + -5r2 = 4r + -7 + -6r2

Reorder the terms:
-15 + -3r + -5r2 = -7 + 4r + -6r2

Solving
-15 + -3r + -5r2 = -7 + 4r + -6r2

Solving for variable 'r'.

Reorder the terms:
-15 + 7 + -3r + -4r + -5r2 + 6r2 = -7 + 4r + -6r2 + 7 + -4r + 6r2

Combine like terms: -15 + 7 = -8
-8 + -3r + -4r + -5r2 + 6r2 = -7 + 4r + -6r2 + 7 + -4r + 6r2

Combine like terms: -3r + -4r = -7r
-8 + -7r + -5r2 + 6r2 = -7 + 4r + -6r2 + 7 + -4r + 6r2

Combine like terms: -5r2 + 6r2 = 1r2
-8 + -7r + 1r2 = -7 + 4r + -6r2 + 7 + -4r + 6r2

Reorder the terms:
-8 + -7r + 1r2 = -7 + 7 + 4r + -4r + -6r2 + 6r2

Combine like terms: -7 + 7 = 0
-8 + -7r + 1r2 = 0 + 4r + -4r + -6r2 + 6r2
-8 + -7r + 1r2 = 4r + -4r + -6r2 + 6r2

Combine like terms: 4r + -4r = 0
-8 + -7r + 1r2 = 0 + -6r2 + 6r2
-8 + -7r + 1r2 = -6r2 + 6r2

Combine like terms: -6r2 + 6r2 = 0
-8 + -7r + 1r2 = 0

Factor a trinomial.
(-1 + -1r)(8 + -1r) = 0


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

Simplifying
-1 + -1r = 0

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

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

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

Divide each side by '-1'.
r = -1

Simplifying
r = -1

Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {-1, 8}

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