r^2-5rx-24x^2=0

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Solution for r^2-5rx-24x^2=0 equation: 


Simplifying
r2 + -5rx + -24x2 = 0

Reorder the terms:
-5rx + r2 + -24x2 = 0

Solving
-5rx + r2 + -24x2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -8x)(r + 3x) = 0


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

Simplifying
r + -8x = 0

Solving
r + -8x = 0

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

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

Combine like terms: -8x + 8x = 0
r + 0 = 0 + 8x
r = 0 + 8x
Remove the zero:
r = 8x

Simplifying
r = 8x

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

Simplifying
r + 3x = 0

Solving
r + 3x = 0

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

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

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

Simplifying
r = -3x
Solution
r = {8x, -3x}

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