(3x-24)(24x-3)=0

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Solution for (3x-24)(24x-3)=0 equation: 


Simplifying
(3x + -24)(24x + -3) = 0

Reorder the terms:
(-24 + 3x)(24x + -3) = 0

Reorder the terms:
(-24 + 3x)(-3 + 24x) = 0

Multiply (-24 + 3x) * (-3 + 24x)
(-24(-3 + 24x) + 3x * (-3 + 24x)) = 0
((-3 * -24 + 24x * -24) + 3x * (-3 + 24x)) = 0
((72 + -576x) + 3x * (-3 + 24x)) = 0
(72 + -576x + (-3 * 3x + 24x * 3x)) = 0
(72 + -576x + (-9x + 72x2)) = 0

Combine like terms: -576x + -9x = -585x
(72 + -585x + 72x2) = 0

Solving
72 + -585x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(8 + -65x + 8x2) = 0

Factor a trinomial.
9((1 + -8x)(8 + -1x)) = 0

Ignore the factor 9.

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

Simplifying
1 + -8x = 0

Solving
1 + -8x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8x = 0 + -1
-8x = 0 + -1

Combine like terms: 0 + -1 = -1
-8x = -1

Divide each side by '-8'.
x = 0.125

Simplifying
x = 0.125

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0.125, 8}

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