7x-(8-17x)x=18

Solution for 7x-(8-17x)x=18 equation:

Simplifying
7x + -1(8 + -17x) * x = 18

Reorder the terms for easier multiplication:
7x + -1x(8 + -17x) = 18
7x + (8 * -1x + -17x * -1x) = 18
7x + (-8x + 17x2) = 18

Combine like terms: 7x + -8x = -1x
-1x + 17x2 = 18

Solving
-1x + 17x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + -1x + 17x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -1x + 17x2 = 0

Factor a trinomial.
(-1 + -1x)(18 + -17x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(18 + -17x)' equal to zero and attempt to solve:

Simplifying
18 + -17x = 0

Solving
18 + -17x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -17x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -17x = 0 + -18
-17x = 0 + -18

Combine like terms: 0 + -18 = -18
-17x = -18

Divide each side by '-17'.
x = 1.058823529

Simplifying
x = 1.058823529
Solution
x = {-1, 1.058823529}