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

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


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

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

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

Multiply (-2 + 6x) * (4 + 3x)
(-2(4 + 3x) + 6x * (4 + 3x)) = 0
((4 * -2 + 3x * -2) + 6x * (4 + 3x)) = 0
((-8 + -6x) + 6x * (4 + 3x)) = 0
(-8 + -6x + (4 * 6x + 3x * 6x)) = 0
(-8 + -6x + (24x + 18x2)) = 0

Combine like terms: -6x + 24x = 18x
(-8 + 18x + 18x2) = 0

Solving
-8 + 18x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 9x + 9x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
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
Solution
x = {-1.333333333, 0.3333333333}

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