(x-2)(x-7)=-6

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Solution for (x-2)(x-7)=-6 equation: 


Simplifying
(x + -2)(x + -7) = -6

Reorder the terms:
(-2 + x)(x + -7) = -6

Reorder the terms:
(-2 + x)(-7 + x) = -6

Multiply (-2 + x) * (-7 + x)
(-2(-7 + x) + x(-7 + x)) = -6
((-7 * -2 + x * -2) + x(-7 + x)) = -6
((14 + -2x) + x(-7 + x)) = -6
(14 + -2x + (-7 * x + x * x)) = -6
(14 + -2x + (-7x + x2)) = -6

Combine like terms: -2x + -7x = -9x
(14 + -9x + x2) = -6

Solving
14 + -9x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
14 + 6 + -9x + x2 = -6 + 6

Combine like terms: 14 + 6 = 20
20 + -9x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
20 + -9x + x2 = 0

Factor a trinomial.
(4 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, 5}

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