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

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


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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
-3 + -2x + 1x2 = 3 + -3 + 5x + -5x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
-3 + -2x + 1x2 = 0 + 5x + -5x + 2x2 + -2x2
-3 + -2x + 1x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
-3 + -2x + 1x2 = 0 + 2x2 + -2x2
-3 + -2x + 1x2 = 2x2 + -2x2

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

Factor a trinomial.
(-1 + -1x)(3 + -1x) = 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 '(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
Solution
x = {-1, 3}

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