(3x-12)(4x-1)=0

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Solution for (3x-12)(4x-1)=0 equation: 


Simplifying
(3x + -12)(4x + -1) = 0

Reorder the terms:
(-12 + 3x)(4x + -1) = 0

Reorder the terms:
(-12 + 3x)(-1 + 4x) = 0

Multiply (-12 + 3x) * (-1 + 4x)
(-12(-1 + 4x) + 3x * (-1 + 4x)) = 0
((-1 * -12 + 4x * -12) + 3x * (-1 + 4x)) = 0
((12 + -48x) + 3x * (-1 + 4x)) = 0
(12 + -48x + (-1 * 3x + 4x * 3x)) = 0
(12 + -48x + (-3x + 12x2)) = 0

Combine like terms: -48x + -3x = -51x
(12 + -51x + 12x2) = 0

Solving
12 + -51x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -17x + 4x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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

Simplifying
4 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.25, 4}

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