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

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


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

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

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

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

Combine like terms: -4x + -1x = -5x
3(4 + -5x + x2) = 0
(4 * 3 + -5x * 3 + x2 * 3) = 0
(12 + -15x + 3x2) = 0

Solving
12 + -15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -5x + x2) = 0

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

Ignore the factor 3.

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

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 = {1, 4}

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