(3x-1)(4x-5)=(2x-1)(6x-7)

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Solution for (3x-1)(4x-5)=(2x-1)(6x-7) equation: 


Simplifying
(3x + -1)(4x + -5) = (2x + -1)(6x + -7)

Reorder the terms:
(-1 + 3x)(4x + -5) = (2x + -1)(6x + -7)

Reorder the terms:
(-1 + 3x)(-5 + 4x) = (2x + -1)(6x + -7)

Multiply (-1 + 3x) * (-5 + 4x)
(-1(-5 + 4x) + 3x * (-5 + 4x)) = (2x + -1)(6x + -7)
((-5 * -1 + 4x * -1) + 3x * (-5 + 4x)) = (2x + -1)(6x + -7)
((5 + -4x) + 3x * (-5 + 4x)) = (2x + -1)(6x + -7)
(5 + -4x + (-5 * 3x + 4x * 3x)) = (2x + -1)(6x + -7)
(5 + -4x + (-15x + 12x2)) = (2x + -1)(6x + -7)

Combine like terms: -4x + -15x = -19x
(5 + -19x + 12x2) = (2x + -1)(6x + -7)

Reorder the terms:
5 + -19x + 12x2 = (-1 + 2x)(6x + -7)

Reorder the terms:
5 + -19x + 12x2 = (-1 + 2x)(-7 + 6x)

Multiply (-1 + 2x) * (-7 + 6x)
5 + -19x + 12x2 = (-1(-7 + 6x) + 2x * (-7 + 6x))
5 + -19x + 12x2 = ((-7 * -1 + 6x * -1) + 2x * (-7 + 6x))
5 + -19x + 12x2 = ((7 + -6x) + 2x * (-7 + 6x))
5 + -19x + 12x2 = (7 + -6x + (-7 * 2x + 6x * 2x))
5 + -19x + 12x2 = (7 + -6x + (-14x + 12x2))

Combine like terms: -6x + -14x = -20x
5 + -19x + 12x2 = (7 + -20x + 12x2)

Add '-12x2' to each side of the equation.
5 + -19x + 12x2 + -12x2 = 7 + -20x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
5 + -19x + 0 = 7 + -20x + 12x2 + -12x2
5 + -19x = 7 + -20x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
5 + -19x = 7 + -20x + 0
5 + -19x = 7 + -20x

Solving
5 + -19x = 7 + -20x

Solving for variable 'x'.

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

Add '20x' to each side of the equation.
5 + -19x + 20x = 7 + -20x + 20x

Combine like terms: -19x + 20x = 1x
5 + 1x = 7 + -20x + 20x

Combine like terms: -20x + 20x = 0
5 + 1x = 7 + 0
5 + 1x = 7

Add '-5' to each side of the equation.
5 + -5 + 1x = 7 + -5

Combine like terms: 5 + -5 = 0
0 + 1x = 7 + -5
1x = 7 + -5

Combine like terms: 7 + -5 = 2
1x = 2

Divide each side by '1'.
x = 2

Simplifying
x = 2

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