2x^2+7x=-6

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

Simplifying
2x2 + 7x = -6

Reorder the terms:
7x + 2x2 = -6

Solving
7x + 2x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 7x + 2x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 7x + 2x2 = 0

Factor a trinomial.
(2 + x)(3 + 2x) = 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 + 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
Solution
x = {-2, -1.5}