43-3x^2=x^2+4x+35

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Solution for 43-3x^2=x^2+4x+35 equation: 


Simplifying
43 + -3x2 = x2 + 4x + 35

Reorder the terms:
43 + -3x2 = 35 + 4x + x2

Solving
43 + -3x2 = 35 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
43 + -35 + -4x + -3x2 + -1x2 = 35 + 4x + x2 + -35 + -4x + -1x2

Combine like terms: 43 + -35 = 8
8 + -4x + -3x2 + -1x2 = 35 + 4x + x2 + -35 + -4x + -1x2

Combine like terms: -3x2 + -1x2 = -4x2
8 + -4x + -4x2 = 35 + 4x + x2 + -35 + -4x + -1x2

Reorder the terms:
8 + -4x + -4x2 = 35 + -35 + 4x + -4x + x2 + -1x2

Combine like terms: 35 + -35 = 0
8 + -4x + -4x2 = 0 + 4x + -4x + x2 + -1x2
8 + -4x + -4x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
8 + -4x + -4x2 = 0 + x2 + -1x2
8 + -4x + -4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -4x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -1x + -1x2) = 0

Factor a trinomial.
4((1 + -1x)(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {1, -2}

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