-(x*x)+30x+17=8x+102

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Solution for -(x*x)+30x+17=8x+102 equation: 


Simplifying
-1(x * x) + 30x + 17 = 8x + 102

Multiply x * x
-1(x2) + 30x + 17 = 8x + 102

Reorder the terms:
17 + 30x + -1x2 = 8x + 102

Reorder the terms:
17 + 30x + -1x2 = 102 + 8x

Solving
17 + 30x + -1x2 = 102 + 8x

Solving for variable 'x'.

Reorder the terms:
17 + -102 + 30x + -8x + -1x2 = 102 + 8x + -102 + -8x

Combine like terms: 17 + -102 = -85
-85 + 30x + -8x + -1x2 = 102 + 8x + -102 + -8x

Combine like terms: 30x + -8x = 22x
-85 + 22x + -1x2 = 102 + 8x + -102 + -8x

Reorder the terms:
-85 + 22x + -1x2 = 102 + -102 + 8x + -8x

Combine like terms: 102 + -102 = 0
-85 + 22x + -1x2 = 0 + 8x + -8x
-85 + 22x + -1x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-85 + 22x + -1x2 = 0

Factor a trinomial.
(-17 + x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-17 + x)' equal to zero and attempt to solve:

Simplifying
-17 + x = 0

Solving
-17 + x = 0

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

Add '17' to each side of the equation.
-17 + 17 + x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + x = 0 + 17
x = 0 + 17

Combine like terms: 0 + 17 = 17
x = 17

Simplifying
x = 17

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {17, 5}

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