x^2-2x-23=3x+1

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Solution for x^2-2x-23=3x+1 equation:


Simplifying
x2 + -2x + -23 = 3x + 1

Reorder the terms:
-23 + -2x + x2 = 3x + 1

Reorder the terms:
-23 + -2x + x2 = 1 + 3x

Solving
-23 + -2x + x2 = 1 + 3x

Solving for variable 'x'.

Reorder the terms:
-23 + -1 + -2x + -3x + x2 = 1 + 3x + -1 + -3x

Combine like terms: -23 + -1 = -24
-24 + -2x + -3x + x2 = 1 + 3x + -1 + -3x

Combine like terms: -2x + -3x = -5x
-24 + -5x + x2 = 1 + 3x + -1 + -3x

Reorder the terms:
-24 + -5x + x2 = 1 + -1 + 3x + -3x

Combine like terms: 1 + -1 = 0
-24 + -5x + x2 = 0 + 3x + -3x
-24 + -5x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-24 + -5x + x2 = 0

Factor a trinomial.
(-3 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3, 8}

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