x^2+x-41=-5x-1

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Solution for x^2+x-41=-5x-1 equation: 


Simplifying
x2 + x + -41 = -5x + -1

Reorder the terms:
-41 + x + x2 = -5x + -1

Reorder the terms:
-41 + x + x2 = -1 + -5x

Solving
-41 + x + x2 = -1 + -5x

Solving for variable 'x'.

Reorder the terms:
-41 + 1 + x + 5x + x2 = -1 + -5x + 1 + 5x

Combine like terms: -41 + 1 = -40
-40 + x + 5x + x2 = -1 + -5x + 1 + 5x

Combine like terms: x + 5x = 6x
-40 + 6x + x2 = -1 + -5x + 1 + 5x

Reorder the terms:
-40 + 6x + x2 = -1 + 1 + -5x + 5x

Combine like terms: -1 + 1 = 0
-40 + 6x + x2 = 0 + -5x + 5x
-40 + 6x + x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-40 + 6x + x2 = 0

Factor a trinomial.
(-10 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
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
Solution
x = {-10, 4}

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