2x(x-3)=(3x-5)(x-3)

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


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

Reorder the terms:
2x(-3 + x) = (3x + -5)(x + -3)
(-3 * 2x + x * 2x) = (3x + -5)(x + -3)
(-6x + 2x2) = (3x + -5)(x + -3)

Reorder the terms:
-6x + 2x2 = (-5 + 3x)(x + -3)

Reorder the terms:
-6x + 2x2 = (-5 + 3x)(-3 + x)

Multiply (-5 + 3x) * (-3 + x)
-6x + 2x2 = (-5(-3 + x) + 3x * (-3 + x))
-6x + 2x2 = ((-3 * -5 + x * -5) + 3x * (-3 + x))
-6x + 2x2 = ((15 + -5x) + 3x * (-3 + x))
-6x + 2x2 = (15 + -5x + (-3 * 3x + x * 3x))
-6x + 2x2 = (15 + -5x + (-9x + 3x2))

Combine like terms: -5x + -9x = -14x
-6x + 2x2 = (15 + -14x + 3x2)

Solving
-6x + 2x2 = 15 + -14x + 3x2

Solving for variable 'x'.

Reorder the terms:
-15 + -6x + 14x + 2x2 + -3x2 = 15 + -14x + 3x2 + -15 + 14x + -3x2

Combine like terms: -6x + 14x = 8x
-15 + 8x + 2x2 + -3x2 = 15 + -14x + 3x2 + -15 + 14x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-15 + 8x + -1x2 = 15 + -14x + 3x2 + -15 + 14x + -3x2

Reorder the terms:
-15 + 8x + -1x2 = 15 + -15 + -14x + 14x + 3x2 + -3x2

Combine like terms: 15 + -15 = 0
-15 + 8x + -1x2 = 0 + -14x + 14x + 3x2 + -3x2
-15 + 8x + -1x2 = -14x + 14x + 3x2 + -3x2

Combine like terms: -14x + 14x = 0
-15 + 8x + -1x2 = 0 + 3x2 + -3x2
-15 + 8x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-15 + 8x + -1x2 = 0

Factor a trinomial.
(-5 + x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

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

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {5, 3}

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