3x^2-18x-42=6

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Solution for 3x^2-18x-42=6 equation:


Simplifying
3x2 + -18x + -42 = 6

Reorder the terms:
-42 + -18x + 3x2 = 6

Solving
-42 + -18x + 3x2 = 6

Solving for variable 'x'.

Reorder the terms:
-42 + -6 + -18x + 3x2 = 6 + -6

Combine like terms: -42 + -6 = -48
-48 + -18x + 3x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-48 + -18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + -6x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(8 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

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

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-2, 8}

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