(4r+7r^2)-(6r^2-6r)=

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Solution for (4r+7r^2)-(6r^2-6r)= equation: 


Simplifying
(4r + 7r2) + -1(6r2 + -6r) = 0

Remove parenthesis around (4r + 7r2)
4r + 7r2 + -1(6r2 + -6r) = 0

Reorder the terms:
4r + 7r2 + -1(-6r + 6r2) = 0
4r + 7r2 + (-6r * -1 + 6r2 * -1) = 0
4r + 7r2 + (6r + -6r2) = 0

Reorder the terms:
4r + 6r + 7r2 + -6r2 = 0

Combine like terms: 4r + 6r = 10r
10r + 7r2 + -6r2 = 0

Combine like terms: 7r2 + -6r2 = 1r2
10r + 1r2 = 0

Solving
10r + 1r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(10 + r) = 0


Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0

Subproblem 2
Set the factor '(10 + r)' equal to zero and attempt to solve:

Simplifying
10 + r = 0

Solving
10 + r = 0

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

Add '-10' to each side of the equation.
10 + -10 + r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + r = 0 + -10
r = 0 + -10

Combine like terms: 0 + -10 = -10
r = -10

Simplifying
r = -10
Solution
r = {0, -10}

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