2r^2t^2+[3rt^2-(-5r^2t^2-8rt^2)]=0

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Solution for 2r^2t^2+[3rt^2-(-5r^2t^2-8rt^2)]=0 equation: 


Simplifying
2r2t2 + [3rt2 + -1(-5r2t2 + -8rt2)] = 0

Reorder the terms:
2r2t2 + [3rt2 + -1(-8rt2 + -5r2t2)] = 0
2r2t2 + [3rt2 + (-8rt2 * -1 + -5r2t2 * -1)] = 0
2r2t2 + [3rt2 + (8rt2 + 5r2t2)] = 0

Combine like terms: 3rt2 + 8rt2 = 11rt2
2r2t2 + [11rt2 + 5r2t2] = 0

Remove brackets around [11rt2 + 5r2t2]
2r2t2 + 11rt2 + 5r2t2 = 0

Reorder the terms:
11rt2 + 2r2t2 + 5r2t2 = 0

Combine like terms: 2r2t2 + 5r2t2 = 7r2t2
11rt2 + 7r2t2 = 0

Solving
11rt2 + 7r2t2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'rt2'.
rt2(11 + 7r) = 0


Subproblem 1
Set the factor 'rt2' equal to zero and attempt to solve:

Simplifying
rt2 = 0

Solving
rt2 = 0

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

Simplifying
rt2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(11 + 7r)' equal to zero and attempt to solve:

Simplifying
11 + 7r = 0

Solving
11 + 7r = 0

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

Add '-11' to each side of the equation.
11 + -11 + 7r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 7r = 0 + -11
7r = 0 + -11

Combine like terms: 0 + -11 = -11
7r = -11

Divide each side by '7'.
r = -1.571428571

Simplifying
r = -1.571428571
Solution
r = {-1.571428571}

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