(-3x+9)(2x-4)=0

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Solution for (-3x+9)(2x-4)=0 equation: 


Simplifying
(-3x + 9)(2x + -4) = 0

Reorder the terms:
(9 + -3x)(2x + -4) = 0

Reorder the terms:
(9 + -3x)(-4 + 2x) = 0

Multiply (9 + -3x) * (-4 + 2x)
(9(-4 + 2x) + -3x * (-4 + 2x)) = 0
((-4 * 9 + 2x * 9) + -3x * (-4 + 2x)) = 0
((-36 + 18x) + -3x * (-4 + 2x)) = 0
(-36 + 18x + (-4 * -3x + 2x * -3x)) = 0
(-36 + 18x + (12x + -6x2)) = 0

Combine like terms: 18x + 12x = 30x
(-36 + 30x + -6x2) = 0

Solving
-36 + 30x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + 5x + -1x2) = 0

Factor a trinomial.
6((-3 + x)(2 + -1x)) = 0

Ignore the factor 6.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {3, 2}

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