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

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


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

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

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

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

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

Solving
8 + -6x + x2 = 0

Solving for variable 'x'.

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

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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