-7r^2+6r-10=3r-8r^2

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Solution for -7r^2+6r-10=3r-8r^2 equation: 


Simplifying
-7r2 + 6r + -10 = 3r + -8r2

Reorder the terms:
-10 + 6r + -7r2 = 3r + -8r2

Solving
-10 + 6r + -7r2 = 3r + -8r2

Solving for variable 'r'.

Reorder the terms:
-10 + 6r + -3r + -7r2 + 8r2 = 3r + -8r2 + -3r + 8r2

Combine like terms: 6r + -3r = 3r
-10 + 3r + -7r2 + 8r2 = 3r + -8r2 + -3r + 8r2

Combine like terms: -7r2 + 8r2 = 1r2
-10 + 3r + 1r2 = 3r + -8r2 + -3r + 8r2

Reorder the terms:
-10 + 3r + 1r2 = 3r + -3r + -8r2 + 8r2

Combine like terms: 3r + -3r = 0
-10 + 3r + 1r2 = 0 + -8r2 + 8r2
-10 + 3r + 1r2 = -8r2 + 8r2

Combine like terms: -8r2 + 8r2 = 0
-10 + 3r + 1r2 = 0

Factor a trinomial.
(-5 + -1r)(2 + -1r) = 0


Subproblem 1
Set the factor '(-5 + -1r)' equal to zero and attempt to solve:

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1r = 0 + 5

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

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

Divide each side by '-1'.
r = -5

Simplifying
r = -5

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 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 + -1r = 0 + -2

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {-5, 2}

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