(x-2)(x-2)-6(x-2)+5=0

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Solution for (x-2)(x-2)-6(x-2)+5=0 equation: 


Simplifying
(x + -2)(x + -2) + -6(x + -2) + 5 = 0

Reorder the terms:
(-2 + x)(x + -2) + -6(x + -2) + 5 = 0

Reorder the terms:
(-2 + x)(-2 + x) + -6(x + -2) + 5 = 0

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) + -6(x + -2) + 5 = 0
((-2 * -2 + x * -2) + x(-2 + x)) + -6(x + -2) + 5 = 0
((4 + -2x) + x(-2 + x)) + -6(x + -2) + 5 = 0
(4 + -2x + (-2 * x + x * x)) + -6(x + -2) + 5 = 0
(4 + -2x + (-2x + x2)) + -6(x + -2) + 5 = 0

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) + -6(x + -2) + 5 = 0

Reorder the terms:
4 + -4x + x2 + -6(-2 + x) + 5 = 0
4 + -4x + x2 + (-2 * -6 + x * -6) + 5 = 0
4 + -4x + x2 + (12 + -6x) + 5 = 0

Reorder the terms:
4 + 12 + 5 + -4x + -6x + x2 = 0

Combine like terms: 4 + 12 = 16
16 + 5 + -4x + -6x + x2 = 0

Combine like terms: 16 + 5 = 21
21 + -4x + -6x + x2 = 0

Combine like terms: -4x + -6x = -10x
21 + -10x + x2 = 0

Solving
21 + -10x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {3, 7}

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