43-3x^2=x^2+12x+27

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Solution for 43-3x^2=x^2+12x+27 equation: 


Simplifying
43 + -3x2 = x2 + 12x + 27

Reorder the terms:
43 + -3x2 = 27 + 12x + x2

Solving
43 + -3x2 = 27 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
43 + -27 + -12x + -3x2 + -1x2 = 27 + 12x + x2 + -27 + -12x + -1x2

Combine like terms: 43 + -27 = 16
16 + -12x + -3x2 + -1x2 = 27 + 12x + x2 + -27 + -12x + -1x2

Combine like terms: -3x2 + -1x2 = -4x2
16 + -12x + -4x2 = 27 + 12x + x2 + -27 + -12x + -1x2

Reorder the terms:
16 + -12x + -4x2 = 27 + -27 + 12x + -12x + x2 + -1x2

Combine like terms: 27 + -27 = 0
16 + -12x + -4x2 = 0 + 12x + -12x + x2 + -1x2
16 + -12x + -4x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
16 + -12x + -4x2 = 0 + x2 + -1x2
16 + -12x + -4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -3x + -1x2) = 0

Factor a trinomial.
4((1 + -1x)(4 + x)) = 0

Ignore the factor 4.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {1, -4}

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