2x(x+4)(6x-3)=0

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Solution for 2x(x+4)(6x-3)=0 equation: 


Simplifying
2x(x + 4)(6x + -3) = 0

Reorder the terms:
2x(4 + x)(6x + -3) = 0

Reorder the terms:
2x(4 + x)(-3 + 6x) = 0

Multiply (4 + x) * (-3 + 6x)
2x(4(-3 + 6x) + x(-3 + 6x)) = 0
2x((-3 * 4 + 6x * 4) + x(-3 + 6x)) = 0
2x((-12 + 24x) + x(-3 + 6x)) = 0
2x(-12 + 24x + (-3 * x + 6x * x)) = 0
2x(-12 + 24x + (-3x + 6x2)) = 0

Combine like terms: 24x + -3x = 21x
2x(-12 + 21x + 6x2) = 0
(-12 * 2x + 21x * 2x + 6x2 * 2x) = 0
(-24x + 42x2 + 12x3) = 0

Solving
-24x + 42x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-4 + 7x + 2x2) = 0

Factor a trinomial.
6x((-4 + -1x)(1 + -2x)) = 0

Ignore the factor 6.

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 '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -4, 0.5}

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