x^2-17x-23=-7x+1

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Solution for x^2-17x-23=-7x+1 equation: 


Simplifying
x2 + -17x + -23 = -7x + 1

Reorder the terms:
-23 + -17x + x2 = -7x + 1

Reorder the terms:
-23 + -17x + x2 = 1 + -7x

Solving
-23 + -17x + x2 = 1 + -7x

Solving for variable 'x'.

Reorder the terms:
-23 + -1 + -17x + 7x + x2 = 1 + -7x + -1 + 7x

Combine like terms: -23 + -1 = -24
-24 + -17x + 7x + x2 = 1 + -7x + -1 + 7x

Combine like terms: -17x + 7x = -10x
-24 + -10x + x2 = 1 + -7x + -1 + 7x

Reorder the terms:
-24 + -10x + x2 = 1 + -1 + -7x + 7x

Combine like terms: 1 + -1 = 0
-24 + -10x + x2 = 0 + -7x + 7x
-24 + -10x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-24 + -10x + x2 = 0

Factor a trinomial.
(-2 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-2, 12}

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