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

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


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

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

Combine like terms: 6x + -3x = 3x
5 + 3x = (3x + -5)(2x + -1)

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

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

Multiply (-5 + 3x) * (-1 + 2x)
5 + 3x = (-5(-1 + 2x) + 3x * (-1 + 2x))
5 + 3x = ((-1 * -5 + 2x * -5) + 3x * (-1 + 2x))
5 + 3x = ((5 + -10x) + 3x * (-1 + 2x))
5 + 3x = (5 + -10x + (-1 * 3x + 2x * 3x))
5 + 3x = (5 + -10x + (-3x + 6x2))

Combine like terms: -10x + -3x = -13x
5 + 3x = (5 + -13x + 6x2)

Add '-5' to each side of the equation.
5 + -5 + 3x = 5 + -13x + -5 + 6x2

Combine like terms: 5 + -5 = 0
0 + 3x = 5 + -13x + -5 + 6x2
3x = 5 + -13x + -5 + 6x2

Reorder the terms:
3x = 5 + -5 + -13x + 6x2

Combine like terms: 5 + -5 = 0
3x = 0 + -13x + 6x2
3x = -13x + 6x2

Solving
3x = -13x + 6x2

Solving for variable 'x'.

Combine like terms: 3x + 13x = 16x
16x + -6x2 = -13x + 6x2 + 13x + -6x2

Reorder the terms:
16x + -6x2 = -13x + 13x + 6x2 + -6x2

Combine like terms: -13x + 13x = 0
16x + -6x2 = 0 + 6x2 + -6x2
16x + -6x2 = 6x2 + -6x2

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(8 + -3x) = 0

Ignore the factor 2.

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 '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {0, 2.666666667}

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