(2z+5)(z+2)=6

Solution for (2z+5)(z+2)=6 equation:

Simplifying
(2z + 5)(z + 2) = 6

Reorder the terms:
(5 + 2z)(z + 2) = 6

Reorder the terms:
(5 + 2z)(2 + z) = 6

Multiply (5 + 2z) * (2 + z)
(5(2 + z) + 2z * (2 + z)) = 6
((2 * 5 + z * 5) + 2z * (2 + z)) = 6
((10 + 5z) + 2z * (2 + z)) = 6
(10 + 5z + (2 * 2z + z * 2z)) = 6
(10 + 5z + (4z + 2z2)) = 6

Combine like terms: 5z + 4z = 9z
(10 + 9z + 2z2) = 6

Solving
10 + 9z + 2z2 = 6

Solving for variable 'z'.

Reorder the terms:
10 + -6 + 9z + 2z2 = 6 + -6

Combine like terms: 10 + -6 = 4
4 + 9z + 2z2 = 6 + -6

Combine like terms: 6 + -6 = 0
4 + 9z + 2z2 = 0

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

Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
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 = {-4, -0.5}