(4x-1)(-6x+12)=0

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Solution for (4x-1)(-6x+12)=0 equation: 


Simplifying
(4x + -1)(-6x + 12) = 0

Reorder the terms:
(-1 + 4x)(-6x + 12) = 0

Reorder the terms:
(-1 + 4x)(12 + -6x) = 0

Multiply (-1 + 4x) * (12 + -6x)
(-1(12 + -6x) + 4x * (12 + -6x)) = 0
((12 * -1 + -6x * -1) + 4x * (12 + -6x)) = 0
((-12 + 6x) + 4x * (12 + -6x)) = 0
(-12 + 6x + (12 * 4x + -6x * 4x)) = 0
(-12 + 6x + (48x + -24x2)) = 0

Combine like terms: 6x + 48x = 54x
(-12 + 54x + -24x2) = 0

Solving
-12 + 54x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 9x + -4x2) = 0

Factor a trinomial.
6((-2 + x)(1 + -4x)) = 0

Ignore the factor 6.

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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

Simplifying
x = 2

Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {2, 0.25}

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