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

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


Simplifying
(6x + -3)(-1x + 3) = 0

Reorder the terms:
(-3 + 6x)(-1x + 3) = 0

Reorder the terms:
(-3 + 6x)(3 + -1x) = 0

Multiply (-3 + 6x) * (3 + -1x)
(-3(3 + -1x) + 6x * (3 + -1x)) = 0
((3 * -3 + -1x * -3) + 6x * (3 + -1x)) = 0
((-9 + 3x) + 6x * (3 + -1x)) = 0
(-9 + 3x + (3 * 6x + -1x * 6x)) = 0
(-9 + 3x + (18x + -6x2)) = 0

Combine like terms: 3x + 18x = 21x
(-9 + 21x + -6x2) = 0

Solving
-9 + 21x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 7x + -2x2) = 0

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

Ignore the factor 3.

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 '(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 = {3, 0.5}

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