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

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


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

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

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

Multiply (2 + 3x) * (2 + x)
(2(2 + x) + 3x * (2 + x)) = 4
((2 * 2 + x * 2) + 3x * (2 + x)) = 4
((4 + 2x) + 3x * (2 + x)) = 4
(4 + 2x + (2 * 3x + x * 3x)) = 4
(4 + 2x + (6x + 3x2)) = 4

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

Add '-4' to each side of the equation.
4 + 8x + -4 + 3x2 = 4 + -4

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

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

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

Solving
8x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + 3x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667
Solution
x = {0, -2.666666667}

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