(-1+3x)(4-6x)=0

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Solution for (-1+3x)(4-6x)=0 equation: 


Simplifying
(-1 + 3x)(4 + -6x) = 0

Multiply (-1 + 3x) * (4 + -6x)
(-1(4 + -6x) + 3x * (4 + -6x)) = 0
((4 * -1 + -6x * -1) + 3x * (4 + -6x)) = 0
((-4 + 6x) + 3x * (4 + -6x)) = 0
(-4 + 6x + (4 * 3x + -6x * 3x)) = 0
(-4 + 6x + (12x + -18x2)) = 0

Combine like terms: 6x + 12x = 18x
(-4 + 18x + -18x2) = 0

Solving
-4 + 18x + -18x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
2((-2 + 3x)(1 + -3x)) = 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 '(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 = {0.6666666667, 0.3333333333}

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