x^2-10x-41=-4x-1

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Solution for x^2-10x-41=-4x-1 equation: 


Simplifying
x2 + -10x + -41 = -4x + -1

Reorder the terms:
-41 + -10x + x2 = -4x + -1

Reorder the terms:
-41 + -10x + x2 = -1 + -4x

Solving
-41 + -10x + x2 = -1 + -4x

Solving for variable 'x'.

Reorder the terms:
-41 + 1 + -10x + 4x + x2 = -1 + -4x + 1 + 4x

Combine like terms: -41 + 1 = -40
-40 + -10x + 4x + x2 = -1 + -4x + 1 + 4x

Combine like terms: -10x + 4x = -6x
-40 + -6x + x2 = -1 + -4x + 1 + 4x

Reorder the terms:
-40 + -6x + x2 = -1 + 1 + -4x + 4x

Combine like terms: -1 + 1 = 0
-40 + -6x + x2 = 0 + -4x + 4x
-40 + -6x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-40 + -6x + x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-4, 10}

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