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

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


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

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

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

Multiply (-2 + x) * (4 + 6x)
(-2(4 + 6x) + x(4 + 6x)) = 0
((4 * -2 + 6x * -2) + x(4 + 6x)) = 0
((-8 + -12x) + x(4 + 6x)) = 0
(-8 + -12x + (4 * x + 6x * x)) = 0
(-8 + -12x + (4x + 6x2)) = 0

Combine like terms: -12x + 4x = -8x
(-8 + -8x + 6x2) = 0

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

Solving for variable 'x'.

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

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

Ignore the factor 2.

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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.6666666667, 2}

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