6(x-4)(6-3x)=0

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Solution for 6(x-4)(6-3x)=0 equation:


Simplifying
6(x + -4)(6 + -3x) = 0

Reorder the terms:
6(-4 + x)(6 + -3x) = 0

Multiply (-4 + x) * (6 + -3x)
6(-4(6 + -3x) + x(6 + -3x)) = 0
6((6 * -4 + -3x * -4) + x(6 + -3x)) = 0
6((-24 + 12x) + x(6 + -3x)) = 0
6(-24 + 12x + (6 * x + -3x * x)) = 0
6(-24 + 12x + (6x + -3x2)) = 0

Combine like terms: 12x + 6x = 18x
6(-24 + 18x + -3x2) = 0
(-24 * 6 + 18x * 6 + -3x2 * 6) = 0
(-144 + 108x + -18x2) = 0

Solving
-144 + 108x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-8 + 6x + -1x2) = 0

Factor a trinomial.
18((-4 + x)(2 + -1x)) = 0

Ignore the factor 18.

Subproblem 1

Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4

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 = {4, 2}

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