(x-2)(x-5)-4=0

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Solution for (x-2)(x-5)-4=0 equation:


Simplifying
(x + -2)(x + -5) + -4 = 0

Reorder the terms:
(-2 + x)(x + -5) + -4 = 0

Reorder the terms:
(-2 + x)(-5 + x) + -4 = 0

Multiply (-2 + x) * (-5 + x)
(-2(-5 + x) + x(-5 + x)) + -4 = 0
((-5 * -2 + x * -2) + x(-5 + x)) + -4 = 0
((10 + -2x) + x(-5 + x)) + -4 = 0
(10 + -2x + (-5 * x + x * x)) + -4 = 0
(10 + -2x + (-5x + x2)) + -4 = 0

Combine like terms: -2x + -5x = -7x
(10 + -7x + x2) + -4 = 0

Reorder the terms:
10 + -4 + -7x + x2 = 0

Combine like terms: 10 + -4 = 6
6 + -7x + x2 = 0

Solving
6 + -7x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

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 = {1, 6}

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