(4x-6)(9-6x)=0

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Solution for (4x-6)(9-6x)=0 equation:


Simplifying
(4x + -6)(9 + -6x) = 0

Reorder the terms:
(-6 + 4x)(9 + -6x) = 0

Multiply (-6 + 4x) * (9 + -6x)
(-6(9 + -6x) + 4x * (9 + -6x)) = 0
((9 * -6 + -6x * -6) + 4x * (9 + -6x)) = 0
((-54 + 36x) + 4x * (9 + -6x)) = 0
(-54 + 36x + (9 * 4x + -6x * 4x)) = 0
(-54 + 36x + (36x + -24x2)) = 0

Combine like terms: 36x + 36x = 72x
(-54 + 72x + -24x2) = 0

Solving
-54 + 72x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-9 + 12x + -4x2) = 0

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

Ignore the factor 6.

Subproblem 1

Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5

Subproblem 2

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {1.5, 1.5}

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