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

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


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

Reorder the terms:
3x(3 + 2x) = 2x + 3
(3 * 3x + 2x * 3x) = 2x + 3
(9x + 6x2) = 2x + 3

Reorder the terms:
9x + 6x2 = 3 + 2x

Solving
9x + 6x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
-3 + 9x + -2x + 6x2 = 3 + 2x + -3 + -2x

Combine like terms: 9x + -2x = 7x
-3 + 7x + 6x2 = 3 + 2x + -3 + -2x

Reorder the terms:
-3 + 7x + 6x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
-3 + 7x + 6x2 = 0 + 2x + -2x
-3 + 7x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + 7x + 6x2 = 0

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


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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, 0.3333333333}

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