6x^2-7xr+2r^2=0

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Solution for 6x^2-7xr+2r^2=0 equation: 


Simplifying
6x2 + -7xr + 2r2 = 0

Reorder the terms:
-7rx + 2r2 + 6x2 = 0

Solving
-7rx + 2r2 + 6x2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -2x)(2r + -3x) = 0


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

Simplifying
r + -2x = 0

Solving
r + -2x = 0

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

Add '2x' to each side of the equation.
r + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
r + 0 = 0 + 2x
r = 0 + 2x
Remove the zero:
r = 2x

Simplifying
r = 2x

Subproblem 2
Set the factor '(2r + -3x)' equal to zero and attempt to solve:

Simplifying
2r + -3x = 0

Solving
2r + -3x = 0

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

Add '3x' to each side of the equation.
2r + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
2r + 0 = 0 + 3x
2r = 0 + 3x
Remove the zero:
2r = 3x

Divide each side by '2'.
r = 1.5x

Simplifying
r = 1.5x
Solution
r = {2x, 1.5x}

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