7x^2+43x=-6

Solution for 7x^2+43x=-6 equation:

Simplifying
7x2 + 43x = -6

Reorder the terms:
43x + 7x2 = -6

Solving
43x + 7x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 43x + 7x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 43x + 7x2 = 0

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

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(1 + 7x)' equal to zero and attempt to solve:

Simplifying
1 + 7x = 0

Solving
1 + 7x = 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 + 7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x = 0 + -1
7x = 0 + -1

Combine like terms: 0 + -1 = -1
7x = -1

Divide each side by '7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
Solution
x = {-6, -0.1428571429}