x^2*2=12x+54

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Solution for x^2*2=12x+54 equation: 


Simplifying
x2 * 2 = 12x + 54

Reorder the terms for easier multiplication:
2x2 = 12x + 54

Reorder the terms:
2x2 = 54 + 12x

Solving
2x2 = 54 + 12x

Solving for variable 'x'.

Reorder the terms:
-54 + -12x + 2x2 = 54 + 12x + -54 + -12x

Reorder the terms:
-54 + -12x + 2x2 = 54 + -54 + 12x + -12x

Combine like terms: 54 + -54 = 0
-54 + -12x + 2x2 = 0 + 12x + -12x
-54 + -12x + 2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-54 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -6x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(9 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
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
Solution
x = {-3, 9}

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