x^2+5x+41=-9x+1

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Solution for x^2+5x+41=-9x+1 equation: 


Simplifying
x2 + 5x + 41 = -9x + 1

Reorder the terms:
41 + 5x + x2 = -9x + 1

Reorder the terms:
41 + 5x + x2 = 1 + -9x

Solving
41 + 5x + x2 = 1 + -9x

Solving for variable 'x'.

Reorder the terms:
41 + -1 + 5x + 9x + x2 = 1 + -9x + -1 + 9x

Combine like terms: 41 + -1 = 40
40 + 5x + 9x + x2 = 1 + -9x + -1 + 9x

Combine like terms: 5x + 9x = 14x
40 + 14x + x2 = 1 + -9x + -1 + 9x

Reorder the terms:
40 + 14x + x2 = 1 + -1 + -9x + 9x

Combine like terms: 1 + -1 = 0
40 + 14x + x2 = 0 + -9x + 9x
40 + 14x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
40 + 14x + x2 = 0

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


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

Simplifying
10 + x = 0

Solving
10 + x = 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 + x = 0 + -10

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

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

Simplifying
x = -10

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-10, -4}

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