x^2-13x+20=-3x-1

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Solution for x^2-13x+20=-3x-1 equation: 


Simplifying
x2 + -13x + 20 = -3x + -1

Reorder the terms:
20 + -13x + x2 = -3x + -1

Reorder the terms:
20 + -13x + x2 = -1 + -3x

Solving
20 + -13x + x2 = -1 + -3x

Solving for variable 'x'.

Reorder the terms:
20 + 1 + -13x + 3x + x2 = -1 + -3x + 1 + 3x

Combine like terms: 20 + 1 = 21
21 + -13x + 3x + x2 = -1 + -3x + 1 + 3x

Combine like terms: -13x + 3x = -10x
21 + -10x + x2 = -1 + -3x + 1 + 3x

Reorder the terms:
21 + -10x + x2 = -1 + 1 + -3x + 3x

Combine like terms: -1 + 1 = 0
21 + -10x + x2 = 0 + -3x + 3x
21 + -10x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
21 + -10x + x2 = 0

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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