2z^2+7z=-6

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

Simplifying
2z2 + 7z = -6

Reorder the terms:
7z + 2z2 = -6

Solving
7z + 2z2 = -6

Solving for variable 'z'.

Reorder the terms:
6 + 7z + 2z2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 7z + 2z2 = 0

Factor a trinomial.
(2 + z)(3 + 2z) = 0

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

Simplifying
2 + z = 0

Solving
2 + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + z = 0 + -2

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

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

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

Simplifying
3 + 2z = 0

Solving
3 + 2z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2z = 0 + -3
2z = 0 + -3

Combine like terms: 0 + -3 = -3
2z = -3

Divide each side by '2'.
z = -1.5

Simplifying
z = -1.5
Solution
z = {-2, -1.5}