7x^2=-10x-3

Solution for 7x^2=-10x-3 equation:

Simplifying
7x2 = -10x + -3

Reorder the terms:
7x2 = -3 + -10x

Solving
7x2 = -3 + -10x

Solving for variable 'x'.

Reorder the terms:
3 + 10x + 7x2 = -3 + -10x + 3 + 10x

Reorder the terms:
3 + 10x + 7x2 = -3 + 3 + -10x + 10x

Combine like terms: -3 + 3 = 0
3 + 10x + 7x2 = 0 + -10x + 10x
3 + 10x + 7x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
3 + 10x + 7x2 = 0

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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
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 = {-1, -0.4285714286}