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

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


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

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

Combine like terms: 2x + 2x = 4x
2 + 4x = 3x(x + 1)

Reorder the terms:
2 + 4x = 3x(1 + x)
2 + 4x = (1 * 3x + x * 3x)
2 + 4x = (3x + 3x2)

Solving
2 + 4x = 3x + 3x2

Solving for variable 'x'.

Combine like terms: 4x + -3x = 1x
2 + 1x + -3x2 = 3x + 3x2 + -3x + -3x2

Reorder the terms:
2 + 1x + -3x2 = 3x + -3x + 3x2 + -3x2

Combine like terms: 3x + -3x = 0
2 + 1x + -3x2 = 0 + 3x2 + -3x2
2 + 1x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
2 + 1x + -3x2 = 0

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


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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {1, -0.6666666667}

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