109-3x^2=x^2+4x+29

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Solution for 109-3x^2=x^2+4x+29 equation: 


Simplifying
109 + -3x2 = x2 + 4x + 29

Reorder the terms:
109 + -3x2 = 29 + 4x + x2

Solving
109 + -3x2 = 29 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
109 + -29 + -4x + -3x2 + -1x2 = 29 + 4x + x2 + -29 + -4x + -1x2

Combine like terms: 109 + -29 = 80
80 + -4x + -3x2 + -1x2 = 29 + 4x + x2 + -29 + -4x + -1x2

Combine like terms: -3x2 + -1x2 = -4x2
80 + -4x + -4x2 = 29 + 4x + x2 + -29 + -4x + -1x2

Reorder the terms:
80 + -4x + -4x2 = 29 + -29 + 4x + -4x + x2 + -1x2

Combine like terms: 29 + -29 = 0
80 + -4x + -4x2 = 0 + 4x + -4x + x2 + -1x2
80 + -4x + -4x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
80 + -4x + -4x2 = 0 + x2 + -1x2
80 + -4x + -4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
80 + -4x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + -1x + -1x2) = 0

Factor a trinomial.
4((4 + -1x)(5 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -5}

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