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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