x^2+12x-43=5x+1

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Solution for x^2+12x-43=5x+1 equation: 


Simplifying
x2 + 12x + -43 = 5x + 1

Reorder the terms:
-43 + 12x + x2 = 5x + 1

Reorder the terms:
-43 + 12x + x2 = 1 + 5x

Solving
-43 + 12x + x2 = 1 + 5x

Solving for variable 'x'.

Reorder the terms:
-43 + -1 + 12x + -5x + x2 = 1 + 5x + -1 + -5x

Combine like terms: -43 + -1 = -44
-44 + 12x + -5x + x2 = 1 + 5x + -1 + -5x

Combine like terms: 12x + -5x = 7x
-44 + 7x + x2 = 1 + 5x + -1 + -5x

Reorder the terms:
-44 + 7x + x2 = 1 + -1 + 5x + -5x

Combine like terms: 1 + -1 = 0
-44 + 7x + x2 = 0 + 5x + -5x
-44 + 7x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-44 + 7x + x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-11, 4}

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