4z^2+3z+2=3

Solution for 4z^2+3z+2=3 equation:

Simplifying
4z2 + 3z + 2 = 3

Reorder the terms:
2 + 3z + 4z2 = 3

Solving
2 + 3z + 4z2 = 3

Solving for variable 'z'.

Reorder the terms:
2 + -3 + 3z + 4z2 = 3 + -3

Combine like terms: 2 + -3 = -1
-1 + 3z + 4z2 = 3 + -3

Combine like terms: 3 + -3 = 0
-1 + 3z + 4z2 = 0

Factor a trinomial.
(-1 + -1z)(1 + -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 '(1 + -4z)' equal to zero and attempt to solve:

Simplifying
1 + -4z = 0

Solving
1 + -4z = 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 + -4z = 0 + -1

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

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

Divide each side by '-4'.
z = 0.25

Simplifying
z = 0.25
Solution
z = {-1, 0.25}