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

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Solution for 2(x-1)(x-4)=0 equation: 


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

Reorder the terms:
2(-1 + x)(x + -4) = 0

Reorder the terms:
2(-1 + x)(-4 + x) = 0

Multiply (-1 + x) * (-4 + x)
2(-1(-4 + x) + x(-4 + x)) = 0
2((-4 * -1 + x * -1) + x(-4 + x)) = 0
2((4 + -1x) + x(-4 + x)) = 0
2(4 + -1x + (-4 * x + x * x)) = 0
2(4 + -1x + (-4x + x2)) = 0

Combine like terms: -1x + -4x = -5x
2(4 + -5x + x2) = 0
(4 * 2 + -5x * 2 + x2 * 2) = 0
(8 + -10x + 2x2) = 0

Solving
8 + -10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -5x + x2) = 0

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

Ignore the factor 2.

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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