x^2-4x-7=-6x+1

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Solution for x^2-4x-7=-6x+1 equation: 


Simplifying
x2 + -4x + -7 = -6x + 1

Reorder the terms:
-7 + -4x + x2 = -6x + 1

Reorder the terms:
-7 + -4x + x2 = 1 + -6x

Solving
-7 + -4x + x2 = 1 + -6x

Solving for variable 'x'.

Reorder the terms:
-7 + -1 + -4x + 6x + x2 = 1 + -6x + -1 + 6x

Combine like terms: -7 + -1 = -8
-8 + -4x + 6x + x2 = 1 + -6x + -1 + 6x

Combine like terms: -4x + 6x = 2x
-8 + 2x + x2 = 1 + -6x + -1 + 6x

Reorder the terms:
-8 + 2x + x2 = 1 + -1 + -6x + 6x

Combine like terms: 1 + -1 = 0
-8 + 2x + x2 = 0 + -6x + 6x
-8 + 2x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-8 + 2x + x2 = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4, 2}

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