2z(2z+13)=14

Solution for 2z(2z+13)=14 equation:

Simplifying
2z(2z + 13) = 14

Reorder the terms:
2z(13 + 2z) = 14
(13 * 2z + 2z * 2z) = 14
(26z + 4z2) = 14

Solving
26z + 4z2 = 14

Solving for variable 'z'.

Reorder the terms:
-14 + 26z + 4z2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 26z + 4z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 13z + 2z2) = 0

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

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

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 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 + -1z = 0 + 7

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

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

Divide each side by '-1'.
z = -7

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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-7, 0.5}