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

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


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

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

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

Multiply (3 + 2x) * (1 + x)
(3(1 + x) + 2x * (1 + x)) = 3x(x + 1)
((1 * 3 + x * 3) + 2x * (1 + x)) = 3x(x + 1)
((3 + 3x) + 2x * (1 + x)) = 3x(x + 1)
(3 + 3x + (1 * 2x + x * 2x)) = 3x(x + 1)
(3 + 3x + (2x + 2x2)) = 3x(x + 1)

Combine like terms: 3x + 2x = 5x
(3 + 5x + 2x2) = 3x(x + 1)

Reorder the terms:
3 + 5x + 2x2 = 3x(1 + x)
3 + 5x + 2x2 = (1 * 3x + x * 3x)
3 + 5x + 2x2 = (3x + 3x2)

Solving
3 + 5x + 2x2 = 3x + 3x2

Solving for variable 'x'.

Reorder the terms:
3 + 5x + -3x + 2x2 + -3x2 = 3x + 3x2 + -3x + -3x2

Combine like terms: 5x + -3x = 2x
3 + 2x + 2x2 + -3x2 = 3x + 3x2 + -3x + -3x2

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

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

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

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

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


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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {3, -1}

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