2z+9=(2z+3)(z+2)

Solution for 2z+9=(2z+3)(z+2) equation:

Simplifying
2z + 9 = (2z + 3)(z + 2)

Reorder the terms:
9 + 2z = (2z + 3)(z + 2)

Reorder the terms:
9 + 2z = (3 + 2z)(z + 2)

Reorder the terms:
9 + 2z = (3 + 2z)(2 + z)

Multiply (3 + 2z) * (2 + z)
9 + 2z = (3(2 + z) + 2z * (2 + z))
9 + 2z = ((2 * 3 + z * 3) + 2z * (2 + z))
9 + 2z = ((6 + 3z) + 2z * (2 + z))
9 + 2z = (6 + 3z + (2 * 2z + z * 2z))
9 + 2z = (6 + 3z + (4z + 2z2))

Combine like terms: 3z + 4z = 7z
9 + 2z = (6 + 7z + 2z2)

Solving
9 + 2z = 6 + 7z + 2z2

Solving for variable 'z'.

Reorder the terms:
9 + -6 + 2z + -7z + -2z2 = 6 + 7z + 2z2 + -6 + -7z + -2z2

Combine like terms: 9 + -6 = 3
3 + 2z + -7z + -2z2 = 6 + 7z + 2z2 + -6 + -7z + -2z2

Combine like terms: 2z + -7z = -5z
3 + -5z + -2z2 = 6 + 7z + 2z2 + -6 + -7z + -2z2

Reorder the terms:
3 + -5z + -2z2 = 6 + -6 + 7z + -7z + 2z2 + -2z2

Combine like terms: 6 + -6 = 0
3 + -5z + -2z2 = 0 + 7z + -7z + 2z2 + -2z2
3 + -5z + -2z2 = 7z + -7z + 2z2 + -2z2

Combine like terms: 7z + -7z = 0
3 + -5z + -2z2 = 0 + 2z2 + -2z2
3 + -5z + -2z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
3 + -5z + -2z2 = 0

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

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

Simplifying
3 + z = 0

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

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

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

Simplifying
z = -3
Solution
z = {0.5, -3}