4z^2+11z+4=7

Solution for 4z^2+11z+4=7 equation:

Simplifying
4z2 + 11z + 4 = 7

Reorder the terms:
4 + 11z + 4z2 = 7

Solving
4 + 11z + 4z2 = 7

Solving for variable 'z'.

Reorder the terms:
4 + -7 + 11z + 4z2 = 7 + -7

Combine like terms: 4 + -7 = -3
-3 + 11z + 4z2 = 7 + -7

Combine like terms: 7 + -7 = 0
-3 + 11z + 4z2 = 0

Factor a trinomial.
(-3 + -1z)(1 + -4z) = 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 '(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 = {-3, 0.25}