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

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


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

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

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

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

Multiply (5 + 3x) * (-1 + x)
-9 + 9x = (5(-1 + x) + 3x * (-1 + x))
-9 + 9x = ((-1 * 5 + x * 5) + 3x * (-1 + x))
-9 + 9x = ((-5 + 5x) + 3x * (-1 + x))
-9 + 9x = (-5 + 5x + (-1 * 3x + x * 3x))
-9 + 9x = (-5 + 5x + (-3x + 3x2))

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

Solving
-9 + 9x = -5 + 2x + 3x2

Solving for variable 'x'.

Reorder the terms:
-9 + 5 + 9x + -2x + -3x2 = -5 + 2x + 3x2 + 5 + -2x + -3x2

Combine like terms: -9 + 5 = -4
-4 + 9x + -2x + -3x2 = -5 + 2x + 3x2 + 5 + -2x + -3x2

Combine like terms: 9x + -2x = 7x
-4 + 7x + -3x2 = -5 + 2x + 3x2 + 5 + -2x + -3x2

Reorder the terms:
-4 + 7x + -3x2 = -5 + 5 + 2x + -2x + 3x2 + -3x2

Combine like terms: -5 + 5 = 0
-4 + 7x + -3x2 = 0 + 2x + -2x + 3x2 + -3x2
-4 + 7x + -3x2 = 2x + -2x + 3x2 + -3x2

Combine like terms: 2x + -2x = 0
-4 + 7x + -3x2 = 0 + 3x2 + -3x2
-4 + 7x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-4 + 7x + -3x2 = 0

Factor a trinomial.
(-4 + 3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-4 + 3x)' equal to zero and attempt to solve:

Simplifying
-4 + 3x = 0

Solving
-4 + 3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3x = 0 + 4
3x = 0 + 4

Combine like terms: 0 + 4 = 4
3x = 4

Divide each side by '3'.
x = 1.333333333

Simplifying
x = 1.333333333

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {1.333333333, 1}

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