(x-9)(x-2)=0

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Solution for (x-9)(x-2)=0 equation:


Simplifying
(x + -9)(x + -2) = 0

Reorder the terms:
(-9 + x)(x + -2) = 0

Reorder the terms:
(-9 + x)(-2 + x) = 0

Multiply (-9 + x) * (-2 + x)
(-9(-2 + x) + x(-2 + x)) = 0
((-2 * -9 + x * -9) + x(-2 + x)) = 0
((18 + -9x) + x(-2 + x)) = 0
(18 + -9x + (-2 * x + x * x)) = 0
(18 + -9x + (-2x + x2)) = 0

Combine like terms: -9x + -2x = -11x
(18 + -11x + x2) = 0

Solving
18 + -11x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9

Solution

x = {2, 9}

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