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

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


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

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

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

Solving
3x + 3x2 = 2 + 2x

Solving for variable 'x'.

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

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

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

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

Combine like terms: 2x + -2x = 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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