x^2+2x+11=-4x+3

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Solution for x^2+2x+11=-4x+3 equation: 


Simplifying
x2 + 2x + 11 = -4x + 3

Reorder the terms:
11 + 2x + x2 = -4x + 3

Reorder the terms:
11 + 2x + x2 = 3 + -4x

Solving
11 + 2x + x2 = 3 + -4x

Solving for variable 'x'.

Reorder the terms:
11 + -3 + 2x + 4x + x2 = 3 + -4x + -3 + 4x

Combine like terms: 11 + -3 = 8
8 + 2x + 4x + x2 = 3 + -4x + -3 + 4x

Combine like terms: 2x + 4x = 6x
8 + 6x + x2 = 3 + -4x + -3 + 4x

Reorder the terms:
8 + 6x + x2 = 3 + -3 + -4x + 4x

Combine like terms: 3 + -3 = 0
8 + 6x + x2 = 0 + -4x + 4x
8 + 6x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
8 + 6x + x2 = 0

Factor a trinomial.
(4 + x)(2 + x) = 0


Subproblem 1
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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-4, -2}

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