-x^2+17x-11=8x+1-4x^2

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Solution for -x^2+17x-11=8x+1-4x^2 equation: 


Simplifying
-1x2 + 17x + -11 = 8x + 1 + -4x2

Reorder the terms:
-11 + 17x + -1x2 = 8x + 1 + -4x2

Reorder the terms:
-11 + 17x + -1x2 = 1 + 8x + -4x2

Solving
-11 + 17x + -1x2 = 1 + 8x + -4x2

Solving for variable 'x'.

Reorder the terms:
-11 + -1 + 17x + -8x + -1x2 + 4x2 = 1 + 8x + -4x2 + -1 + -8x + 4x2

Combine like terms: -11 + -1 = -12
-12 + 17x + -8x + -1x2 + 4x2 = 1 + 8x + -4x2 + -1 + -8x + 4x2

Combine like terms: 17x + -8x = 9x
-12 + 9x + -1x2 + 4x2 = 1 + 8x + -4x2 + -1 + -8x + 4x2

Combine like terms: -1x2 + 4x2 = 3x2
-12 + 9x + 3x2 = 1 + 8x + -4x2 + -1 + -8x + 4x2

Reorder the terms:
-12 + 9x + 3x2 = 1 + -1 + 8x + -8x + -4x2 + 4x2

Combine like terms: 1 + -1 = 0
-12 + 9x + 3x2 = 0 + 8x + -8x + -4x2 + 4x2
-12 + 9x + 3x2 = 8x + -8x + -4x2 + 4x2

Combine like terms: 8x + -8x = 0
-12 + 9x + 3x2 = 0 + -4x2 + 4x2
-12 + 9x + 3x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-12 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 3x + x2) = 0

Factor a trinomial.
3((-4 + -1x)(1 + -1x)) = 0

Ignore the factor 3.

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 '(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
Solution
x = {-4, 1}

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