4x(x-6)(5x-8)=0

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Solution for 4x(x-6)(5x-8)=0 equation: 


Simplifying
4x(x + -6)(5x + -8) = 0

Reorder the terms:
4x(-6 + x)(5x + -8) = 0

Reorder the terms:
4x(-6 + x)(-8 + 5x) = 0

Multiply (-6 + x) * (-8 + 5x)
4x(-6(-8 + 5x) + x(-8 + 5x)) = 0
4x((-8 * -6 + 5x * -6) + x(-8 + 5x)) = 0
4x((48 + -30x) + x(-8 + 5x)) = 0
4x(48 + -30x + (-8 * x + 5x * x)) = 0
4x(48 + -30x + (-8x + 5x2)) = 0

Combine like terms: -30x + -8x = -38x
4x(48 + -38x + 5x2) = 0
(48 * 4x + -38x * 4x + 5x2 * 4x) = 0
(192x + -152x2 + 20x3) = 0

Solving
192x + -152x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(48 + -38x + 5x2) = 0

Factor a trinomial.
4x((8 + -5x)(6 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 1.6, 6}

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