4z^2=z+5

Solution for 4z^2=z+5 equation:

Simplifying
4z2 = z + 5

Reorder the terms:
4z2 = 5 + z

Solving
4z2 = 5 + z

Solving for variable 'z'.

Reorder the terms:
-5 + -1z + 4z2 = 5 + z + -5 + -1z

Reorder the terms:
-5 + -1z + 4z2 = 5 + -5 + z + -1z

Combine like terms: 5 + -5 = 0
-5 + -1z + 4z2 = 0 + z + -1z
-5 + -1z + 4z2 = z + -1z

Combine like terms: z + -1z = 0
-5 + -1z + 4z2 = 0

Factor a trinomial.
(-1 + -1z)(5 + -4z) = 0

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

Simplifying
-1 + -1z = 0

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

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

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

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

Simplifying
z = -1
Subproblem 2
Set the factor '(5 + -4z)' equal to zero and attempt to solve:

Simplifying
5 + -4z = 0

Solving
5 + -4z = 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 + -4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4z = 0 + -5
-4z = 0 + -5

Combine like terms: 0 + -5 = -5
-4z = -5

Divide each side by '-4'.
z = 1.25

Simplifying
z = 1.25
Solution
z = {-1, 1.25}