17(x+3)+17x(x+5)=170

Solution for 17(x+3)+17x(x+5)=170 equation:

Simplifying
17(x + 3) + 17x(x + 5) = 170

Reorder the terms:
17(3 + x) + 17x(x + 5) = 170
(3 * 17 + x * 17) + 17x(x + 5) = 170
(51 + 17x) + 17x(x + 5) = 170

Reorder the terms:
51 + 17x + 17x(5 + x) = 170
51 + 17x + (5 * 17x + x * 17x) = 170
51 + 17x + (85x + 17x2) = 170

Combine like terms: 17x + 85x = 102x
51 + 102x + 17x2 = 170

Solving
51 + 102x + 17x2 = 170

Solving for variable 'x'.

Reorder the terms:
51 + -170 + 102x + 17x2 = 170 + -170

Combine like terms: 51 + -170 = -119
-119 + 102x + 17x2 = 170 + -170

Combine like terms: 170 + -170 = 0
-119 + 102x + 17x2 = 0

Factor out the Greatest Common Factor (GCF), '17'.
17(-7 + 6x + x2) = 0

Factor a trinomial.
17((-7 + -1x)(1 + -1x)) = 0

Ignore the factor 17.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
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 = {-7, 1}