10x^2+27x+1=-17

Solution for 10x^2+27x+1=-17 equation:

Simplifying
10x2 + 27x + 1 = -17

Reorder the terms:
1 + 27x + 10x2 = -17

Solving
1 + 27x + 10x2 = -17

Solving for variable 'x'.

Reorder the terms:
1 + 17 + 27x + 10x2 = -17 + 17

Combine like terms: 1 + 17 = 18
18 + 27x + 10x2 = -17 + 17

Combine like terms: -17 + 17 = 0
18 + 27x + 10x2 = 0

Factor a trinomial.
(3 + 2x)(6 + 5x) = 0

Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2
Solution
x = {-1.5, -1.2}