8x+x(x-6)=57-(17-x^2)

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Solution for 8x+x(x-6)=57-(17-x^2) equation: 


Simplifying
8x + x(x + -6) = 57 + -1(17 + -1x2)

Reorder the terms:
8x + x(-6 + x) = 57 + -1(17 + -1x2)
8x + (-6 * x + x * x) = 57 + -1(17 + -1x2)
8x + (-6x + x2) = 57 + -1(17 + -1x2)

Combine like terms: 8x + -6x = 2x
2x + x2 = 57 + -1(17 + -1x2)
2x + x2 = 57 + (17 * -1 + -1x2 * -1)
2x + x2 = 57 + (-17 + 1x2)

Combine like terms: 57 + -17 = 40
2x + x2 = 40 + 1x2

Solving
2x + x2 = 40 + 1x2

Solving for variable 'x'.

Reorder the terms:
-40 + 2x + x2 + -1x2 = 40 + 1x2 + -40 + -1x2

Combine like terms: x2 + -1x2 = 0
-40 + 2x + 0 = 40 + 1x2 + -40 + -1x2
-40 + 2x = 40 + 1x2 + -40 + -1x2

Reorder the terms:
-40 + 2x = 40 + -40 + 1x2 + -1x2

Combine like terms: 40 + -40 = 0
-40 + 2x = 0 + 1x2 + -1x2
-40 + 2x = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-40 + 2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + x)' equal to zero and attempt to solve:

Simplifying
-20 + x = 0

Solving
-20 + x = 0

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

Add '20' to each side of the equation.
-20 + 20 + x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + x = 0 + 20
x = 0 + 20

Combine like terms: 0 + 20 = 20
x = 20

Simplifying
x = 20
Solution
x = {20}

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