(2z+6)4z-3=5z+12

Solution for (2z+6)4z-3=5z+12 equation:

Simplifying
(2z + 6) * 4z + -3 = 5z + 12

Reorder the terms:
(6 + 2z) * 4z + -3 = 5z + 12

Reorder the terms for easier multiplication:
4z(6 + 2z) + -3 = 5z + 12
(6 * 4z + 2z * 4z) + -3 = 5z + 12
(24z + 8z2) + -3 = 5z + 12

Reorder the terms:
-3 + 24z + 8z2 = 5z + 12

Reorder the terms:
-3 + 24z + 8z2 = 12 + 5z

Solving
-3 + 24z + 8z2 = 12 + 5z

Solving for variable 'z'.

Reorder the terms:
-3 + -12 + 24z + -5z + 8z2 = 12 + 5z + -12 + -5z

Combine like terms: -3 + -12 = -15
-15 + 24z + -5z + 8z2 = 12 + 5z + -12 + -5z

Combine like terms: 24z + -5z = 19z
-15 + 19z + 8z2 = 12 + 5z + -12 + -5z

Reorder the terms:
-15 + 19z + 8z2 = 12 + -12 + 5z + -5z

Combine like terms: 12 + -12 = 0
-15 + 19z + 8z2 = 0 + 5z + -5z
-15 + 19z + 8z2 = 5z + -5z

Combine like terms: 5z + -5z = 0
-15 + 19z + 8z2 = 0

Factor a trinomial.
(-3 + -1z)(5 + -8z) = 0

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

Simplifying
-3 + -1z = 0

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

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

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

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(5 + -8z)' equal to zero and attempt to solve:

Simplifying
5 + -8z = 0

Solving
5 + -8z = 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 + -8z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8z = 0 + -5
-8z = 0 + -5

Combine like terms: 0 + -5 = -5
-8z = -5

Divide each side by '-8'.
z = 0.625

Simplifying
z = 0.625
Solution
z = {-3, 0.625}