0=2z^2+13z+21

Solution for 0=2z^2+13z+21 equation:

Simplifying
0 = 2z2 + 13z + 21

Reorder the terms:
0 = 21 + 13z + 2z2

Solving
0 = 21 + 13z + 2z2

Solving for variable 'z'.

Combine like terms: 0 + -21 = -21
-21 + -13z + -2z2 = 21 + 13z + 2z2 + -21 + -13z + -2z2

Reorder the terms:
-21 + -13z + -2z2 = 21 + -21 + 13z + -13z + 2z2 + -2z2

Combine like terms: 21 + -21 = 0
-21 + -13z + -2z2 = 0 + 13z + -13z + 2z2 + -2z2
-21 + -13z + -2z2 = 13z + -13z + 2z2 + -2z2

Combine like terms: 13z + -13z = 0
-21 + -13z + -2z2 = 0 + 2z2 + -2z2
-21 + -13z + -2z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
-21 + -13z + -2z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 13z + 2z2) = 0

Factor a trinomial.
-1((7 + 2z)(3 + z)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 2z)' equal to zero and attempt to solve:

Simplifying
7 + 2z = 0

Solving
7 + 2z = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2z = 0 + -7

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

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

Divide each side by '2'.
z = -3.5

Simplifying
z = -3.5
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 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 + z = 0 + -3

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

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

Simplifying
z = -3
Solution
z = {-3.5, -3}