54x-84=6x^2

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Solution for 54x-84=6x^2 equation:


Simplifying
54x + -84 = 6x2

Reorder the terms:
-84 + 54x = 6x2

Solving
-84 + 54x = 6x2

Solving for variable 'x'.

Combine like terms: 6x2 + -6x2 = 0
-84 + 54x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-14 + 9x + -1x2) = 0

Factor a trinomial.
6((-7 + x)(2 + -1x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7

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 = {7, 2}

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