x^2+6x+41=-7x+5

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Solution for x^2+6x+41=-7x+5 equation: 


Simplifying
x2 + 6x + 41 = -7x + 5

Reorder the terms:
41 + 6x + x2 = -7x + 5

Reorder the terms:
41 + 6x + x2 = 5 + -7x

Solving
41 + 6x + x2 = 5 + -7x

Solving for variable 'x'.

Reorder the terms:
41 + -5 + 6x + 7x + x2 = 5 + -7x + -5 + 7x

Combine like terms: 41 + -5 = 36
36 + 6x + 7x + x2 = 5 + -7x + -5 + 7x

Combine like terms: 6x + 7x = 13x
36 + 13x + x2 = 5 + -7x + -5 + 7x

Reorder the terms:
36 + 13x + x2 = 5 + -5 + -7x + 7x

Combine like terms: 5 + -5 = 0
36 + 13x + x2 = 0 + -7x + 7x
36 + 13x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
36 + 13x + x2 = 0

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


Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9

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 = {-9, -4}

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