(3x-1)(2x+4)-(3x-1)(x+1)=(3x-1)(2x-3)

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Solution for (3x-1)(2x+4)-(3x-1)(x+1)=(3x-1)(2x-3) equation: 


Simplifying
(3x + -1)(2x + 4) + -1(3x + -1)(x + 1) = (3x + -1)(2x + -3)

Reorder the terms:
(-1 + 3x)(2x + 4) + -1(3x + -1)(x + 1) = (3x + -1)(2x + -3)

Reorder the terms:
(-1 + 3x)(4 + 2x) + -1(3x + -1)(x + 1) = (3x + -1)(2x + -3)

Multiply (-1 + 3x) * (4 + 2x)
(-1(4 + 2x) + 3x * (4 + 2x)) + -1(3x + -1)(x + 1) = (3x + -1)(2x + -3)
((4 * -1 + 2x * -1) + 3x * (4 + 2x)) + -1(3x + -1)(x + 1) = (3x + -1)(2x + -3)
((-4 + -2x) + 3x * (4 + 2x)) + -1(3x + -1)(x + 1) = (3x + -1)(2x + -3)
(-4 + -2x + (4 * 3x + 2x * 3x)) + -1(3x + -1)(x + 1) = (3x + -1)(2x + -3)
(-4 + -2x + (12x + 6x2)) + -1(3x + -1)(x + 1) = (3x + -1)(2x + -3)

Combine like terms: -2x + 12x = 10x
(-4 + 10x + 6x2) + -1(3x + -1)(x + 1) = (3x + -1)(2x + -3)

Reorder the terms:
-4 + 10x + 6x2 + -1(-1 + 3x)(x + 1) = (3x + -1)(2x + -3)

Reorder the terms:
-4 + 10x + 6x2 + -1(-1 + 3x)(1 + x) = (3x + -1)(2x + -3)

Multiply (-1 + 3x) * (1 + x)
-4 + 10x + 6x2 + -1(-1(1 + x) + 3x * (1 + x)) = (3x + -1)(2x + -3)
-4 + 10x + 6x2 + -1((1 * -1 + x * -1) + 3x * (1 + x)) = (3x + -1)(2x + -3)
-4 + 10x + 6x2 + -1((-1 + -1x) + 3x * (1 + x)) = (3x + -1)(2x + -3)
-4 + 10x + 6x2 + -1(-1 + -1x + (1 * 3x + x * 3x)) = (3x + -1)(2x + -3)
-4 + 10x + 6x2 + -1(-1 + -1x + (3x + 3x2)) = (3x + -1)(2x + -3)

Combine like terms: -1x + 3x = 2x
-4 + 10x + 6x2 + -1(-1 + 2x + 3x2) = (3x + -1)(2x + -3)
-4 + 10x + 6x2 + (-1 * -1 + 2x * -1 + 3x2 * -1) = (3x + -1)(2x + -3)
-4 + 10x + 6x2 + (1 + -2x + -3x2) = (3x + -1)(2x + -3)

Reorder the terms:
-4 + 1 + 10x + -2x + 6x2 + -3x2 = (3x + -1)(2x + -3)

Combine like terms: -4 + 1 = -3
-3 + 10x + -2x + 6x2 + -3x2 = (3x + -1)(2x + -3)

Combine like terms: 10x + -2x = 8x
-3 + 8x + 6x2 + -3x2 = (3x + -1)(2x + -3)

Combine like terms: 6x2 + -3x2 = 3x2
-3 + 8x + 3x2 = (3x + -1)(2x + -3)

Reorder the terms:
-3 + 8x + 3x2 = (-1 + 3x)(2x + -3)

Reorder the terms:
-3 + 8x + 3x2 = (-1 + 3x)(-3 + 2x)

Multiply (-1 + 3x) * (-3 + 2x)
-3 + 8x + 3x2 = (-1(-3 + 2x) + 3x * (-3 + 2x))
-3 + 8x + 3x2 = ((-3 * -1 + 2x * -1) + 3x * (-3 + 2x))
-3 + 8x + 3x2 = ((3 + -2x) + 3x * (-3 + 2x))
-3 + 8x + 3x2 = (3 + -2x + (-3 * 3x + 2x * 3x))
-3 + 8x + 3x2 = (3 + -2x + (-9x + 6x2))

Combine like terms: -2x + -9x = -11x
-3 + 8x + 3x2 = (3 + -11x + 6x2)

Solving
-3 + 8x + 3x2 = 3 + -11x + 6x2

Solving for variable 'x'.

Reorder the terms:
-3 + -3 + 8x + 11x + 3x2 + -6x2 = 3 + -11x + 6x2 + -3 + 11x + -6x2

Combine like terms: -3 + -3 = -6
-6 + 8x + 11x + 3x2 + -6x2 = 3 + -11x + 6x2 + -3 + 11x + -6x2

Combine like terms: 8x + 11x = 19x
-6 + 19x + 3x2 + -6x2 = 3 + -11x + 6x2 + -3 + 11x + -6x2

Combine like terms: 3x2 + -6x2 = -3x2
-6 + 19x + -3x2 = 3 + -11x + 6x2 + -3 + 11x + -6x2

Reorder the terms:
-6 + 19x + -3x2 = 3 + -3 + -11x + 11x + 6x2 + -6x2

Combine like terms: 3 + -3 = 0
-6 + 19x + -3x2 = 0 + -11x + 11x + 6x2 + -6x2
-6 + 19x + -3x2 = -11x + 11x + 6x2 + -6x2

Combine like terms: -11x + 11x = 0
-6 + 19x + -3x2 = 0 + 6x2 + -6x2
-6 + 19x + -3x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-6 + 19x + -3x2 = 0

Factor a trinomial.
(-6 + x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6

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 = {6, 0.3333333333}

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