x^2-3x-43=4x+1

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Solution for x^2-3x-43=4x+1 equation: 


Simplifying
x2 + -3x + -43 = 4x + 1

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

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

Solving
-43 + -3x + x2 = 1 + 4x

Solving for variable 'x'.

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

Combine like terms: -43 + -1 = -44
-44 + -3x + -4x + x2 = 1 + 4x + -1 + -4x

Combine like terms: -3x + -4x = -7x
-44 + -7x + x2 = 1 + 4x + -1 + -4x

Reorder the terms:
-44 + -7x + x2 = 1 + -1 + 4x + -4x

Combine like terms: 1 + -1 = 0
-44 + -7x + x2 = 0 + 4x + -4x
-44 + -7x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-44 + -7x + x2 = 0

Factor a trinomial.
(-4 + -1x)(11 + -1x) = 0


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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-4, 11}

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