7x^2=-17x-6

Solution for 7x^2=-17x-6 equation:

Simplifying
7x2 = -17x + -6

Reorder the terms:
7x2 = -6 + -17x

Solving
7x2 = -6 + -17x

Solving for variable 'x'.

Reorder the terms:
6 + 17x + 7x2 = -6 + -17x + 6 + 17x

Reorder the terms:
6 + 17x + 7x2 = -6 + 6 + -17x + 17x

Combine like terms: -6 + 6 = 0
6 + 17x + 7x2 = 0 + -17x + 17x
6 + 17x + 7x2 = -17x + 17x

Combine like terms: -17x + 17x = 0
6 + 17x + 7x2 = 0

Factor a trinomial.
(2 + x)(3 + 7x) = 0

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + 7x)' equal to zero and attempt to solve:

Simplifying
3 + 7x = 0

Solving
3 + 7x = 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 + 7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7x = 0 + -3
7x = 0 + -3

Combine like terms: 0 + -3 = -3
7x = -3

Divide each side by '7'.
x = -0.4285714286

Simplifying
x = -0.4285714286
Solution
x = {-2, -0.4285714286}