5x^2=-6-17x

Solution for 5x^2=-6-17x equation:

Simplifying
5x2 = -6 + -17x

Solving
5x2 = -6 + -17x

Solving for variable 'x'.

Reorder the terms:
6 + 17x + 5x2 = -6 + -17x + 6 + 17x

Reorder the terms:
6 + 17x + 5x2 = -6 + 6 + -17x + 17x

Combine like terms: -6 + 6 = 0
6 + 17x + 5x2 = 0 + -17x + 17x
6 + 17x + 5x2 = -17x + 17x

Combine like terms: -17x + 17x = 0
6 + 17x + 5x2 = 0

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

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Subproblem 2
Set the factor '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {-3, -0.4}