x^2+5x+19=-4x+5

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Solution for x^2+5x+19=-4x+5 equation: 


Simplifying
x2 + 5x + 19 = -4x + 5

Reorder the terms:
19 + 5x + x2 = -4x + 5

Reorder the terms:
19 + 5x + x2 = 5 + -4x

Solving
19 + 5x + x2 = 5 + -4x

Solving for variable 'x'.

Reorder the terms:
19 + -5 + 5x + 4x + x2 = 5 + -4x + -5 + 4x

Combine like terms: 19 + -5 = 14
14 + 5x + 4x + x2 = 5 + -4x + -5 + 4x

Combine like terms: 5x + 4x = 9x
14 + 9x + x2 = 5 + -4x + -5 + 4x

Reorder the terms:
14 + 9x + x2 = 5 + -5 + -4x + 4x

Combine like terms: 5 + -5 = 0
14 + 9x + x2 = 0 + -4x + 4x
14 + 9x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
14 + 9x + x2 = 0

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


Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

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 = {-7, -2}

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