(3x-1)(5x-1)=(5x-7)(3x+2)

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


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

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

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

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

Combine like terms: -5x + -3x = -8x
(1 + -8x + 15x2) = (5x + -7)(3x + 2)

Reorder the terms:
1 + -8x + 15x2 = (-7 + 5x)(3x + 2)

Reorder the terms:
1 + -8x + 15x2 = (-7 + 5x)(2 + 3x)

Multiply (-7 + 5x) * (2 + 3x)
1 + -8x + 15x2 = (-7(2 + 3x) + 5x * (2 + 3x))
1 + -8x + 15x2 = ((2 * -7 + 3x * -7) + 5x * (2 + 3x))
1 + -8x + 15x2 = ((-14 + -21x) + 5x * (2 + 3x))
1 + -8x + 15x2 = (-14 + -21x + (2 * 5x + 3x * 5x))
1 + -8x + 15x2 = (-14 + -21x + (10x + 15x2))

Combine like terms: -21x + 10x = -11x
1 + -8x + 15x2 = (-14 + -11x + 15x2)

Add '-15x2' to each side of the equation.
1 + -8x + 15x2 + -15x2 = -14 + -11x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
1 + -8x + 0 = -14 + -11x + 15x2 + -15x2
1 + -8x = -14 + -11x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
1 + -8x = -14 + -11x + 0
1 + -8x = -14 + -11x

Solving
1 + -8x = -14 + -11x

Solving for variable 'x'.

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

Add '11x' to each side of the equation.
1 + -8x + 11x = -14 + -11x + 11x

Combine like terms: -8x + 11x = 3x
1 + 3x = -14 + -11x + 11x

Combine like terms: -11x + 11x = 0
1 + 3x = -14 + 0
1 + 3x = -14

Add '-1' to each side of the equation.
1 + -1 + 3x = -14 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = -14 + -1
3x = -14 + -1

Combine like terms: -14 + -1 = -15
3x = -15

Divide each side by '3'.
x = -5

Simplifying
x = -5

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