2z(3z+14)=10

Solution for 2z(3z+14)=10 equation:

Simplifying
2z(3z + 14) = 10

Reorder the terms:
2z(14 + 3z) = 10
(14 * 2z + 3z * 2z) = 10
(28z + 6z2) = 10

Solving
28z + 6z2 = 10

Solving for variable 'z'.

Reorder the terms:
-10 + 28z + 6z2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 28z + 6z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 14z + 3z2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 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 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5
Subproblem 2
Set the factor '(1 + -3z)' equal to zero and attempt to solve:

Simplifying
1 + -3z = 0

Solving
1 + -3z = 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 + -3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3z = 0 + -1
-3z = 0 + -1

Combine like terms: 0 + -1 = -1
-3z = -1

Divide each side by '-3'.
z = 0.3333333333

Simplifying
z = 0.3333333333
Solution
z = {-5, 0.3333333333}