8x+(2x-5)(3x-1)=(6x-5)(2x-1)

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Solution for 8x+(2x-5)(3x-1)=(6x-5)(2x-1) equation: 


Simplifying
8x + (2x + -5)(3x + -1) = (6x + -5)(2x + -1)

Reorder the terms:
8x + (-5 + 2x)(3x + -1) = (6x + -5)(2x + -1)

Reorder the terms:
8x + (-5 + 2x)(-1 + 3x) = (6x + -5)(2x + -1)

Multiply (-5 + 2x) * (-1 + 3x)
8x + (-5(-1 + 3x) + 2x * (-1 + 3x)) = (6x + -5)(2x + -1)
8x + ((-1 * -5 + 3x * -5) + 2x * (-1 + 3x)) = (6x + -5)(2x + -1)
8x + ((5 + -15x) + 2x * (-1 + 3x)) = (6x + -5)(2x + -1)
8x + (5 + -15x + (-1 * 2x + 3x * 2x)) = (6x + -5)(2x + -1)
8x + (5 + -15x + (-2x + 6x2)) = (6x + -5)(2x + -1)

Combine like terms: -15x + -2x = -17x
8x + (5 + -17x + 6x2) = (6x + -5)(2x + -1)

Reorder the terms:
5 + 8x + -17x + 6x2 = (6x + -5)(2x + -1)

Combine like terms: 8x + -17x = -9x
5 + -9x + 6x2 = (6x + -5)(2x + -1)

Reorder the terms:
5 + -9x + 6x2 = (-5 + 6x)(2x + -1)

Reorder the terms:
5 + -9x + 6x2 = (-5 + 6x)(-1 + 2x)

Multiply (-5 + 6x) * (-1 + 2x)
5 + -9x + 6x2 = (-5(-1 + 2x) + 6x * (-1 + 2x))
5 + -9x + 6x2 = ((-1 * -5 + 2x * -5) + 6x * (-1 + 2x))
5 + -9x + 6x2 = ((5 + -10x) + 6x * (-1 + 2x))
5 + -9x + 6x2 = (5 + -10x + (-1 * 6x + 2x * 6x))
5 + -9x + 6x2 = (5 + -10x + (-6x + 12x2))

Combine like terms: -10x + -6x = -16x
5 + -9x + 6x2 = (5 + -16x + 12x2)

Add '-5' to each side of the equation.
5 + -9x + -5 + 6x2 = 5 + -16x + -5 + 12x2

Reorder the terms:
5 + -5 + -9x + 6x2 = 5 + -16x + -5 + 12x2

Combine like terms: 5 + -5 = 0
0 + -9x + 6x2 = 5 + -16x + -5 + 12x2
-9x + 6x2 = 5 + -16x + -5 + 12x2

Reorder the terms:
-9x + 6x2 = 5 + -5 + -16x + 12x2

Combine like terms: 5 + -5 = 0
-9x + 6x2 = 0 + -16x + 12x2
-9x + 6x2 = -16x + 12x2

Solving
-9x + 6x2 = -16x + 12x2

Solving for variable 'x'.

Reorder the terms:
-9x + 16x + 6x2 + -12x2 = -16x + 12x2 + 16x + -12x2

Combine like terms: -9x + 16x = 7x
7x + 6x2 + -12x2 = -16x + 12x2 + 16x + -12x2

Combine like terms: 6x2 + -12x2 = -6x2
7x + -6x2 = -16x + 12x2 + 16x + -12x2

Reorder the terms:
7x + -6x2 = -16x + 16x + 12x2 + -12x2

Combine like terms: -16x + 16x = 0
7x + -6x2 = 0 + 12x2 + -12x2
7x + -6x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
7x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -6x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {0, 1.166666667}

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