6(2-x)94(-3+6x)=0

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Solution for 6(2-x)94(-3+6x)=0 equation:


Simplifying
6(2 + -1x) * 94(-3 + 6x) = 0

Reorder the terms for easier multiplication:
6 * 94(2 + -1x)(-3 + 6x) = 0

Multiply 6 * 94
564(2 + -1x)(-3 + 6x) = 0

Multiply (2 + -1x) * (-3 + 6x)
564(2(-3 + 6x) + -1x * (-3 + 6x)) = 0
564((-3 * 2 + 6x * 2) + -1x * (-3 + 6x)) = 0
564((-6 + 12x) + -1x * (-3 + 6x)) = 0
564(-6 + 12x + (-3 * -1x + 6x * -1x)) = 0
564(-6 + 12x + (3x + -6x2)) = 0

Combine like terms: 12x + 3x = 15x
564(-6 + 15x + -6x2) = 0
(-6 * 564 + 15x * 564 + -6x2 * 564) = 0
(-3384 + 8460x + -3384x2) = 0

Solving
-3384 + 8460x + -3384x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '1692'.
1692(-2 + 5x + -2x2) = 0

Factor a trinomial.
1692((-2 + x)(1 + -2x)) = 0

Ignore the factor 1692.

Subproblem 1

Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {2, 0.5}

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