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

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


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

Reorder the terms:
6x(-4 + x) + 2(x + -4) = 0
(-4 * 6x + x * 6x) + 2(x + -4) = 0
(-24x + 6x2) + 2(x + -4) = 0

Reorder the terms:
-24x + 6x2 + 2(-4 + x) = 0
-24x + 6x2 + (-4 * 2 + x * 2) = 0
-24x + 6x2 + (-8 + 2x) = 0

Reorder the terms:
-8 + -24x + 2x + 6x2 = 0

Combine like terms: -24x + 2x = -22x
-8 + -22x + 6x2 = 0

Solving
-8 + -22x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -11x + 3x2) = 0

Factor a trinomial.
2((-1 + -3x)(4 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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 = {-0.3333333333, 4}

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