(3x-2)(6x+1)=0

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Solution for (3x-2)(6x+1)=0 equation: 


Simplifying
(3x + -2)(6x + 1) = 0

Reorder the terms:
(-2 + 3x)(6x + 1) = 0

Reorder the terms:
(-2 + 3x)(1 + 6x) = 0

Multiply (-2 + 3x) * (1 + 6x)
(-2(1 + 6x) + 3x * (1 + 6x)) = 0
((1 * -2 + 6x * -2) + 3x * (1 + 6x)) = 0
((-2 + -12x) + 3x * (1 + 6x)) = 0
(-2 + -12x + (1 * 3x + 6x * 3x)) = 0
(-2 + -12x + (3x + 18x2)) = 0

Combine like terms: -12x + 3x = -9x
(-2 + -9x + 18x2) = 0

Solving
-2 + -9x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -6x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 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 + -6x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x = 0 + 1
-6x = 0 + 1

Combine like terms: 0 + 1 = 1
-6x = 1

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667

Subproblem 2
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
Solution
x = {-0.1666666667, 0.6666666667}

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