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

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


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

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

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

Multiply (-4 + x) * (-5 + x)
(-4(-5 + x) + x(-5 + x)) = 2
((-5 * -4 + x * -4) + x(-5 + x)) = 2
((20 + -4x) + x(-5 + x)) = 2
(20 + -4x + (-5 * x + x * x)) = 2
(20 + -4x + (-5x + x2)) = 2

Combine like terms: -4x + -5x = -9x
(20 + -9x + x2) = 2

Solving
20 + -9x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
20 + -2 + -9x + x2 = 2 + -2

Combine like terms: 20 + -2 = 18
18 + -9x + x2 = 2 + -2

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

Factor a trinomial.
(3 + -1x)(6 + -1x) = 0

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {3, 6}

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