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

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


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

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

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

Multiply (-5 + x) * (-2 + x)
(-5(-2 + x) + x(-2 + x)) = 0
((-2 * -5 + x * -5) + x(-2 + x)) = 0
((10 + -5x) + x(-2 + x)) = 0
(10 + -5x + (-2 * x + x * x)) = 0
(10 + -5x + (-2x + x2)) = 0

Combine like terms: -5x + -2x = -7x
(10 + -7x + x2) = 0

Solving
10 + -7x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {2, 5}

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