(3x-9)(8x-2)=0

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Solution for (3x-9)(8x-2)=0 equation: 


Simplifying
(3x + -9)(8x + -2) = 0

Reorder the terms:
(-9 + 3x)(8x + -2) = 0

Reorder the terms:
(-9 + 3x)(-2 + 8x) = 0

Multiply (-9 + 3x) * (-2 + 8x)
(-9(-2 + 8x) + 3x * (-2 + 8x)) = 0
((-2 * -9 + 8x * -9) + 3x * (-2 + 8x)) = 0
((18 + -72x) + 3x * (-2 + 8x)) = 0
(18 + -72x + (-2 * 3x + 8x * 3x)) = 0
(18 + -72x + (-6x + 24x2)) = 0

Combine like terms: -72x + -6x = -78x
(18 + -78x + 24x2) = 0

Solving
18 + -78x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -13x + 4x2) = 0

Factor a trinomial.
6((1 + -4x)(3 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.25, 3}

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