4z^2+19z+2=7

Solution for 4z^2+19z+2=7 equation:

Simplifying
4z2 + 19z + 2 = 7

Reorder the terms:
2 + 19z + 4z2 = 7

Solving
2 + 19z + 4z2 = 7

Solving for variable 'z'.

Reorder the terms:
2 + -7 + 19z + 4z2 = 7 + -7

Combine like terms: 2 + -7 = -5
-5 + 19z + 4z2 = 7 + -7

Combine like terms: 7 + -7 = 0
-5 + 19z + 4z2 = 0

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

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

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 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 + -1z = 0 + 5

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

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

Divide each side by '-1'.
z = -5

Simplifying
z = -5
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 = {-5, 0.25}