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

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


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

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

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

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

Combine like terms: 10x + 3x = 13x
(2 + 13x + 15x2) = (5x + 7)(3x + -1)

Reorder the terms:
2 + 13x + 15x2 = (7 + 5x)(3x + -1)

Reorder the terms:
2 + 13x + 15x2 = (7 + 5x)(-1 + 3x)

Multiply (7 + 5x) * (-1 + 3x)
2 + 13x + 15x2 = (7(-1 + 3x) + 5x * (-1 + 3x))
2 + 13x + 15x2 = ((-1 * 7 + 3x * 7) + 5x * (-1 + 3x))
2 + 13x + 15x2 = ((-7 + 21x) + 5x * (-1 + 3x))
2 + 13x + 15x2 = (-7 + 21x + (-1 * 5x + 3x * 5x))
2 + 13x + 15x2 = (-7 + 21x + (-5x + 15x2))

Combine like terms: 21x + -5x = 16x
2 + 13x + 15x2 = (-7 + 16x + 15x2)

Add '-15x2' to each side of the equation.
2 + 13x + 15x2 + -15x2 = -7 + 16x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
2 + 13x + 0 = -7 + 16x + 15x2 + -15x2
2 + 13x = -7 + 16x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
2 + 13x = -7 + 16x + 0
2 + 13x = -7 + 16x

Solving
2 + 13x = -7 + 16x

Solving for variable 'x'.

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

Add '-16x' to each side of the equation.
2 + 13x + -16x = -7 + 16x + -16x

Combine like terms: 13x + -16x = -3x
2 + -3x = -7 + 16x + -16x

Combine like terms: 16x + -16x = 0
2 + -3x = -7 + 0
2 + -3x = -7

Add '-2' to each side of the equation.
2 + -2 + -3x = -7 + -2

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

Combine like terms: -7 + -2 = -9
-3x = -9

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

Simplifying
x = 3

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