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

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Solution for 5(x-2)(x-4)=0 equation: 


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

Reorder the terms:
5(-2 + x)(x + -4) = 0

Reorder the terms:
5(-2 + x)(-4 + x) = 0

Multiply (-2 + x) * (-4 + x)
5(-2(-4 + x) + x(-4 + x)) = 0
5((-4 * -2 + x * -2) + x(-4 + x)) = 0
5((8 + -2x) + x(-4 + x)) = 0
5(8 + -2x + (-4 * x + x * x)) = 0
5(8 + -2x + (-4x + x2)) = 0

Combine like terms: -2x + -4x = -6x
5(8 + -6x + x2) = 0
(8 * 5 + -6x * 5 + x2 * 5) = 0
(40 + -30x + 5x2) = 0

Solving
40 + -30x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(8 + -6x + x2) = 0

Factor a trinomial.
5((2 + -1x)(4 + -1x)) = 0

Ignore the factor 5.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 4}

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