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

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


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

Reorder the terms:
3x(-3 + x) = 5(3 + -1x)
(-3 * 3x + x * 3x) = 5(3 + -1x)
(-9x + 3x2) = 5(3 + -1x)
-9x + 3x2 = (3 * 5 + -1x * 5)
-9x + 3x2 = (15 + -5x)

Solving
-9x + 3x2 = 15 + -5x

Solving for variable 'x'.

Reorder the terms:
-15 + -9x + 5x + 3x2 = 15 + -5x + -15 + 5x

Combine like terms: -9x + 5x = -4x
-15 + -4x + 3x2 = 15 + -5x + -15 + 5x

Reorder the terms:
-15 + -4x + 3x2 = 15 + -15 + -5x + 5x

Combine like terms: 15 + -15 = 0
-15 + -4x + 3x2 = 0 + -5x + 5x
-15 + -4x + 3x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-15 + -4x + 3x2 = 0

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


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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 = {-1.666666667, 3}

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