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

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


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

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

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

Solving
3x + 3x2 = 2 + 4x

Solving for variable 'x'.

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

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

Reorder the terms:
-2 + -1x + 3x2 = 2 + -2 + 4x + -4x

Combine like terms: 2 + -2 = 0
-2 + -1x + 3x2 = 0 + 4x + -4x
-2 + -1x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-2 + -1x + 3x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.6666666667, 1}

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