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

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


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

Reorder the terms:
3(-5 + 3x) = (3x + 3)(x + -2)
(-5 * 3 + 3x * 3) = (3x + 3)(x + -2)
(-15 + 9x) = (3x + 3)(x + -2)

Reorder the terms:
-15 + 9x = (3 + 3x)(x + -2)

Reorder the terms:
-15 + 9x = (3 + 3x)(-2 + x)

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

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

Solving
-15 + 9x = -6 + -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
-15 + 6 + 9x + 3x + -3x2 = -6 + -3x + 3x2 + 6 + 3x + -3x2

Combine like terms: -15 + 6 = -9
-9 + 9x + 3x + -3x2 = -6 + -3x + 3x2 + 6 + 3x + -3x2

Combine like terms: 9x + 3x = 12x
-9 + 12x + -3x2 = -6 + -3x + 3x2 + 6 + 3x + -3x2

Reorder the terms:
-9 + 12x + -3x2 = -6 + 6 + -3x + 3x + 3x2 + -3x2

Combine like terms: -6 + 6 = 0
-9 + 12x + -3x2 = 0 + -3x + 3x + 3x2 + -3x2
-9 + 12x + -3x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
-9 + 12x + -3x2 = 0 + 3x2 + -3x2
-9 + 12x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-9 + 12x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 4x + -1x2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3

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 = {3, 1}

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