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

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


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

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

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

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

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

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

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

Multiply (-1 + 2x) * (3 + x)
-1 + 2x + 3x2 = (-1(3 + x) + 2x * (3 + x))
-1 + 2x + 3x2 = ((3 * -1 + x * -1) + 2x * (3 + x))
-1 + 2x + 3x2 = ((-3 + -1x) + 2x * (3 + x))
-1 + 2x + 3x2 = (-3 + -1x + (3 * 2x + x * 2x))
-1 + 2x + 3x2 = (-3 + -1x + (6x + 2x2))

Combine like terms: -1x + 6x = 5x
-1 + 2x + 3x2 = (-3 + 5x + 2x2)

Solving
-1 + 2x + 3x2 = -3 + 5x + 2x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Factor a trinomial.
(1 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}

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