x^2+4x+1=3x+7

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Solution for x^2+4x+1=3x+7 equation: 


Simplifying
x2 + 4x + 1 = 3x + 7

Reorder the terms:
1 + 4x + x2 = 3x + 7

Reorder the terms:
1 + 4x + x2 = 7 + 3x

Solving
1 + 4x + x2 = 7 + 3x

Solving for variable 'x'.

Reorder the terms:
1 + -7 + 4x + -3x + x2 = 7 + 3x + -7 + -3x

Combine like terms: 1 + -7 = -6
-6 + 4x + -3x + x2 = 7 + 3x + -7 + -3x

Combine like terms: 4x + -3x = 1x
-6 + 1x + x2 = 7 + 3x + -7 + -3x

Reorder the terms:
-6 + 1x + x2 = 7 + -7 + 3x + -3x

Combine like terms: 7 + -7 = 0
-6 + 1x + x2 = 0 + 3x + -3x
-6 + 1x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-6 + 1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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