2z(2z+7)-30=0

Solution for 2z(2z+7)-30=0 equation:

Simplifying
2z(2z + 7) + -30 = 0

Reorder the terms:
2z(7 + 2z) + -30 = 0
(7 * 2z + 2z * 2z) + -30 = 0
(14z + 4z2) + -30 = 0

Reorder the terms:
-30 + 14z + 4z2 = 0

Solving
-30 + 14z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 7z + 2z2) = 0

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