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

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


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

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

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

Combine like terms: 2x + 15x = 17x
(-5 + 17x + -6x2) = (x + -7)(3 + -6x)

Reorder the terms:
-5 + 17x + -6x2 = (-7 + x)(3 + -6x)

Multiply (-7 + x) * (3 + -6x)
-5 + 17x + -6x2 = (-7(3 + -6x) + x(3 + -6x))
-5 + 17x + -6x2 = ((3 * -7 + -6x * -7) + x(3 + -6x))
-5 + 17x + -6x2 = ((-21 + 42x) + x(3 + -6x))
-5 + 17x + -6x2 = (-21 + 42x + (3 * x + -6x * x))
-5 + 17x + -6x2 = (-21 + 42x + (3x + -6x2))

Combine like terms: 42x + 3x = 45x
-5 + 17x + -6x2 = (-21 + 45x + -6x2)

Add '6x2' to each side of the equation.
-5 + 17x + -6x2 + 6x2 = -21 + 45x + -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-5 + 17x + 0 = -21 + 45x + -6x2 + 6x2
-5 + 17x = -21 + 45x + -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-5 + 17x = -21 + 45x + 0
-5 + 17x = -21 + 45x

Solving
-5 + 17x = -21 + 45x

Solving for variable 'x'.

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

Add '-45x' to each side of the equation.
-5 + 17x + -45x = -21 + 45x + -45x

Combine like terms: 17x + -45x = -28x
-5 + -28x = -21 + 45x + -45x

Combine like terms: 45x + -45x = 0
-5 + -28x = -21 + 0
-5 + -28x = -21

Add '5' to each side of the equation.
-5 + 5 + -28x = -21 + 5

Combine like terms: -5 + 5 = 0
0 + -28x = -21 + 5
-28x = -21 + 5

Combine like terms: -21 + 5 = -16
-28x = -16

Divide each side by '-28'.
x = 0.5714285714

Simplifying
x = 0.5714285714

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