(3-x)(x-2)=0

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Solution for (3-x)(x-2)=0 equation:


Simplifying
(3 + -1x)(x + -2) = 0

Reorder the terms:
(3 + -1x)(-2 + x) = 0

Multiply (3 + -1x) * (-2 + x)
(3(-2 + x) + -1x * (-2 + x)) = 0
((-2 * 3 + x * 3) + -1x * (-2 + x)) = 0
((-6 + 3x) + -1x * (-2 + x)) = 0
(-6 + 3x + (-2 * -1x + x * -1x)) = 0
(-6 + 3x + (2x + -1x2)) = 0

Combine like terms: 3x + 2x = 5x
(-6 + 5x + -1x2) = 0

Solving
-6 + 5x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3

Subproblem 2

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

Solution

x = {3, 2}

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