10x^2=-17x-3

Solution for 10x^2=-17x-3 equation:

Simplifying
10x2 = -17x + -3

Reorder the terms:
10x2 = -3 + -17x

Solving
10x2 = -3 + -17x

Solving for variable 'x'.

Reorder the terms:
3 + 17x + 10x2 = -3 + -17x + 3 + 17x

Reorder the terms:
3 + 17x + 10x2 = -3 + 3 + -17x + 17x

Combine like terms: -3 + 3 = 0
3 + 17x + 10x2 = 0 + -17x + 17x
3 + 17x + 10x2 = -17x + 17x

Combine like terms: -17x + 17x = 0
3 + 17x + 10x2 = 0

Factor a trinomial.
(3 + 2x)(1 + 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 '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-1.5, -0.2}