x^2+11x+19=4x+7

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Solution for x^2+11x+19=4x+7 equation: 


Simplifying
x2 + 11x + 19 = 4x + 7

Reorder the terms:
19 + 11x + x2 = 4x + 7

Reorder the terms:
19 + 11x + x2 = 7 + 4x

Solving
19 + 11x + x2 = 7 + 4x

Solving for variable 'x'.

Reorder the terms:
19 + -7 + 11x + -4x + x2 = 7 + 4x + -7 + -4x

Combine like terms: 19 + -7 = 12
12 + 11x + -4x + x2 = 7 + 4x + -7 + -4x

Combine like terms: 11x + -4x = 7x
12 + 7x + x2 = 7 + 4x + -7 + -4x

Reorder the terms:
12 + 7x + x2 = 7 + -7 + 4x + -4x

Combine like terms: 7 + -7 = 0
12 + 7x + x2 = 0 + 4x + -4x
12 + 7x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
12 + 7x + x2 = 0

Factor a trinomial.
(4 + x)(3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-4, -3}

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