8x-21=(x^2)+4x-17

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Solution for 8x-21=(x^2)+4x-17 equation: 


Simplifying
8x + -21 = (x2) + 4x + -17

Reorder the terms:
-21 + 8x = (x2) + 4x + -17
-21 + 8x = x2 + 4x + -17

Reorder the terms:
-21 + 8x = -17 + 4x + x2

Solving
-21 + 8x = -17 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
-21 + 17 + 8x + -4x + -1x2 = -17 + 4x + x2 + 17 + -4x + -1x2

Combine like terms: -21 + 17 = -4
-4 + 8x + -4x + -1x2 = -17 + 4x + x2 + 17 + -4x + -1x2

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

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

Combine like terms: -17 + 17 = 0
-4 + 4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
-4 + 4x + -1x2 = 4x + -4x + x2 + -1x2

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

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

Factor a trinomial.
(-2 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

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

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

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

Simplifying
x = 2

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 = {2, 2}

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