(3x-6)(5x-8)=0

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Solution for (3x-6)(5x-8)=0 equation: 


Simplifying
(3x + -6)(5x + -8) = 0

Reorder the terms:
(-6 + 3x)(5x + -8) = 0

Reorder the terms:
(-6 + 3x)(-8 + 5x) = 0

Multiply (-6 + 3x) * (-8 + 5x)
(-6(-8 + 5x) + 3x * (-8 + 5x)) = 0
((-8 * -6 + 5x * -6) + 3x * (-8 + 5x)) = 0
((48 + -30x) + 3x * (-8 + 5x)) = 0
(48 + -30x + (-8 * 3x + 5x * 3x)) = 0
(48 + -30x + (-24x + 15x2)) = 0

Combine like terms: -30x + -24x = -54x
(48 + -54x + 15x2) = 0

Solving
48 + -54x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + -18x + 5x2) = 0

Factor a trinomial.
3((8 + -5x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 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 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.6, 2}

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