2x(3x+5)*(6x-8)=0

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Solution for 2x(3x+5)*(6x-8)=0 equation:


Simplifying
2x(3x + 5)(6x + -8) = 0

Reorder the terms:
2x(5 + 3x)(6x + -8) = 0

Reorder the terms:
2x(5 + 3x)(-8 + 6x) = 0

Multiply (5 + 3x) * (-8 + 6x)
2x(5(-8 + 6x) + 3x * (-8 + 6x)) = 0
2x((-8 * 5 + 6x * 5) + 3x * (-8 + 6x)) = 0
2x((-40 + 30x) + 3x * (-8 + 6x)) = 0
2x(-40 + 30x + (-8 * 3x + 6x * 3x)) = 0
2x(-40 + 30x + (-24x + 18x2)) = 0

Combine like terms: 30x + -24x = 6x
2x(-40 + 6x + 18x2) = 0
(-40 * 2x + 6x * 2x + 18x2 * 2x) = 0
(-80x + 12x2 + 36x3) = 0

Solving
-80x + 12x2 + 36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-20 + 3x + 9x2) = 0

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

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

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, -1.666666667, 1.333333333}

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