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

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


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

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

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

Multiply (2 + 4x) * (-4 + x)
3(2(-4 + x) + 4x * (-4 + x)) = 0
3((-4 * 2 + x * 2) + 4x * (-4 + x)) = 0
3((-8 + 2x) + 4x * (-4 + x)) = 0
3(-8 + 2x + (-4 * 4x + x * 4x)) = 0
3(-8 + 2x + (-16x + 4x2)) = 0

Combine like terms: 2x + -16x = -14x
3(-8 + -14x + 4x2) = 0
(-8 * 3 + -14x * 3 + 4x2 * 3) = 0
(-24 + -42x + 12x2) = 0

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

Solving for variable 'x'.

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

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

Ignore the factor 6.

Subproblem 1
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

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
Solution
x = {-0.5, 4}

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