(2z-1)(z+3)=15

Solution for (2z-1)(z+3)=15 equation:

Simplifying
(2z + -1)(z + 3) = 15

Reorder the terms:
(-1 + 2z)(z + 3) = 15

Reorder the terms:
(-1 + 2z)(3 + z) = 15

Multiply (-1 + 2z) * (3 + z)
(-1(3 + z) + 2z * (3 + z)) = 15
((3 * -1 + z * -1) + 2z * (3 + z)) = 15
((-3 + -1z) + 2z * (3 + z)) = 15
(-3 + -1z + (3 * 2z + z * 2z)) = 15
(-3 + -1z + (6z + 2z2)) = 15

Combine like terms: -1z + 6z = 5z
(-3 + 5z + 2z2) = 15

Solving
-3 + 5z + 2z2 = 15

Solving for variable 'z'.

Reorder the terms:
-3 + -15 + 5z + 2z2 = 15 + -15

Combine like terms: -3 + -15 = -18
-18 + 5z + 2z2 = 15 + -15

Combine like terms: 15 + -15 = 0
-18 + 5z + 2z2 = 0

Factor a trinomial.
(-9 + -2z)(2 + -1z) = 0

Subproblem 1
Set the factor '(-9 + -2z)' equal to zero and attempt to solve:

Simplifying
-9 + -2z = 0

Solving
-9 + -2z = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2z = 0 + 9
-2z = 0 + 9

Combine like terms: 0 + 9 = 9
-2z = 9

Divide each side by '-2'.
z = -4.5

Simplifying
z = -4.5
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

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

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-4.5, 2}