4z^2+9=12z

Solution for 4z^2+9=12z equation:

Simplifying
4z2 + 9 = 12z

Reorder the terms:
9 + 4z2 = 12z

Solving
9 + 4z2 = 12z

Solving for variable 'z'.

Reorder the terms:
9 + -12z + 4z2 = 12z + -12z

Combine like terms: 12z + -12z = 0
9 + -12z + 4z2 = 0

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

Subproblem 1
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
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 = {1.5, 1.5}