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

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


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

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

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

Multiply (-5 + 3x) * (-6 + 8x)
(-5(-6 + 8x) + 3x * (-6 + 8x)) = 0
((-6 * -5 + 8x * -5) + 3x * (-6 + 8x)) = 0
((30 + -40x) + 3x * (-6 + 8x)) = 0
(30 + -40x + (-6 * 3x + 8x * 3x)) = 0
(30 + -40x + (-18x + 24x2)) = 0

Combine like terms: -40x + -18x = -58x
(30 + -58x + 24x2) = 0

Solving
30 + -58x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -29x + 12x2) = 0

Factor a trinomial.
2((3 + -4x)(5 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0.75, 1.666666667}

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