(3x+2)(x+1)=4

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Solution for (3x+2)(x+1)=4 equation: 


Simplifying
(3x + 2)(x + 1) = 4

Reorder the terms:
(2 + 3x)(x + 1) = 4

Reorder the terms:
(2 + 3x)(1 + x) = 4

Multiply (2 + 3x) * (1 + x)
(2(1 + x) + 3x * (1 + x)) = 4
((1 * 2 + x * 2) + 3x * (1 + x)) = 4
((2 + 2x) + 3x * (1 + x)) = 4
(2 + 2x + (1 * 3x + x * 3x)) = 4
(2 + 2x + (3x + 3x2)) = 4

Combine like terms: 2x + 3x = 5x
(2 + 5x + 3x2) = 4

Solving
2 + 5x + 3x2 = 4

Solving for variable 'x'.

Reorder the terms:
2 + -4 + 5x + 3x2 = 4 + -4

Combine like terms: 2 + -4 = -2
-2 + 5x + 3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-2 + 5x + 3x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-2, 0.3333333333}

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