(3x-1)(2x-5)=(3x-1)(x+2)

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Solution for (3x-1)(2x-5)=(3x-1)(x+2) equation: 


Simplifying
(3x + -1)(2x + -5) = (3x + -1)(x + 2)

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

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

Multiply (-1 + 3x) * (-5 + 2x)
(-1(-5 + 2x) + 3x * (-5 + 2x)) = (3x + -1)(x + 2)
((-5 * -1 + 2x * -1) + 3x * (-5 + 2x)) = (3x + -1)(x + 2)
((5 + -2x) + 3x * (-5 + 2x)) = (3x + -1)(x + 2)
(5 + -2x + (-5 * 3x + 2x * 3x)) = (3x + -1)(x + 2)
(5 + -2x + (-15x + 6x2)) = (3x + -1)(x + 2)

Combine like terms: -2x + -15x = -17x
(5 + -17x + 6x2) = (3x + -1)(x + 2)

Reorder the terms:
5 + -17x + 6x2 = (-1 + 3x)(x + 2)

Reorder the terms:
5 + -17x + 6x2 = (-1 + 3x)(2 + x)

Multiply (-1 + 3x) * (2 + x)
5 + -17x + 6x2 = (-1(2 + x) + 3x * (2 + x))
5 + -17x + 6x2 = ((2 * -1 + x * -1) + 3x * (2 + x))
5 + -17x + 6x2 = ((-2 + -1x) + 3x * (2 + x))
5 + -17x + 6x2 = (-2 + -1x + (2 * 3x + x * 3x))
5 + -17x + 6x2 = (-2 + -1x + (6x + 3x2))

Combine like terms: -1x + 6x = 5x
5 + -17x + 6x2 = (-2 + 5x + 3x2)

Solving
5 + -17x + 6x2 = -2 + 5x + 3x2

Solving for variable 'x'.

Reorder the terms:
5 + 2 + -17x + -5x + 6x2 + -3x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Combine like terms: 5 + 2 = 7
7 + -17x + -5x + 6x2 + -3x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Combine like terms: -17x + -5x = -22x
7 + -22x + 6x2 + -3x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Combine like terms: 6x2 + -3x2 = 3x2
7 + -22x + 3x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Reorder the terms:
7 + -22x + 3x2 = -2 + 2 + 5x + -5x + 3x2 + -3x2

Combine like terms: -2 + 2 = 0
7 + -22x + 3x2 = 0 + 5x + -5x + 3x2 + -3x2
7 + -22x + 3x2 = 5x + -5x + 3x2 + -3x2

Combine like terms: 5x + -5x = 0
7 + -22x + 3x2 = 0 + 3x2 + -3x2
7 + -22x + 3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
7 + -22x + 3x2 = 0

Factor a trinomial.
(1 + -3x)(7 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0.3333333333, 7}

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