x^2-3x^2+27=6x+7

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Solution for x^2-3x^2+27=6x+7 equation: 


Simplifying
x2 + -3x2 + 27 = 6x + 7

Reorder the terms:
27 + x2 + -3x2 = 6x + 7

Combine like terms: x2 + -3x2 = -2x2
27 + -2x2 = 6x + 7

Reorder the terms:
27 + -2x2 = 7 + 6x

Solving
27 + -2x2 = 7 + 6x

Solving for variable 'x'.

Reorder the terms:
27 + -7 + -6x + -2x2 = 7 + 6x + -7 + -6x

Combine like terms: 27 + -7 = 20
20 + -6x + -2x2 = 7 + 6x + -7 + -6x

Reorder the terms:
20 + -6x + -2x2 = 7 + -7 + 6x + -6x

Combine like terms: 7 + -7 = 0
20 + -6x + -2x2 = 0 + 6x + -6x
20 + -6x + -2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
20 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -3x + -1x2) = 0

Factor a trinomial.
2((2 + -1x)(5 + x)) = 0

Ignore the factor 2.

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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {2, -5}

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