10x^2=-17x-6

Solution for 10x^2=-17x-6 equation:

Simplifying
10x2 = -17x + -6

Reorder the terms:
10x2 = -6 + -17x

Solving
10x2 = -6 + -17x

Solving for variable 'x'.

Reorder the terms:
6 + 17x + 10x2 = -6 + -17x + 6 + 17x

Reorder the terms:
6 + 17x + 10x2 = -6 + 6 + -17x + 17x

Combine like terms: -6 + 6 = 0
6 + 17x + 10x2 = 0 + -17x + 17x
6 + 17x + 10x2 = -17x + 17x

Combine like terms: -17x + 17x = 0
6 + 17x + 10x2 = 0

Factor a trinomial.
(6 + 5x)(1 + 2x) = 0

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1.2, -0.5}