3x^2-36x+108=675

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Solution for 3x^2-36x+108=675 equation:


Simplifying
3x2 + -36x + 108 = 675

Reorder the terms:
108 + -36x + 3x2 = 675

Solving
108 + -36x + 3x2 = 675

Solving for variable 'x'.

Reorder the terms:
108 + -675 + -36x + 3x2 = 675 + -675

Combine like terms: 108 + -675 = -567
-567 + -36x + 3x2 = 675 + -675

Combine like terms: 675 + -675 = 0
-567 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-189 + -12x + x2) = 0

Factor a trinomial.
3((-9 + -1x)(21 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(21 + -1x)' equal to zero and attempt to solve: Simplifying 21 + -1x = 0 Solving 21 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1x = 0 + -21 -1x = 0 + -21 Combine like terms: 0 + -21 = -21 -1x = -21 Divide each side by '-1'. x = 21 Simplifying x = 21

Solution

x = {-9, 21}

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