=2z^2+13z+15

Solution for =2z^2+13z+15 equation:

Simplifying
0 = 2z2 + 13z + 15

Reorder the terms:
0 = 15 + 13z + 2z2

Solving
0 = 15 + 13z + 2z2

Solving for variable 'z'.

Combine like terms: 0 + -15 = -15
-15 + -13z + -2z2 = 15 + 13z + 2z2 + -15 + -13z + -2z2

Reorder the terms:
-15 + -13z + -2z2 = 15 + -15 + 13z + -13z + 2z2 + -2z2

Combine like terms: 15 + -15 = 0
-15 + -13z + -2z2 = 0 + 13z + -13z + 2z2 + -2z2
-15 + -13z + -2z2 = 13z + -13z + 2z2 + -2z2

Combine like terms: 13z + -13z = 0
-15 + -13z + -2z2 = 0 + 2z2 + -2z2
-15 + -13z + -2z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
-15 + -13z + -2z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 13z + 2z2) = 0

Factor a trinomial.
-1((5 + z)(3 + 2z)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
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 = {-5, -1.5}