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

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


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

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

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

Combine like terms: 12x + 18x = 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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