=7z^2-4z-3

Solution for =7z^2-4z-3 equation:

Simplifying
0 = 7z2 + -4z + -3

Reorder the terms:
0 = -3 + -4z + 7z2

Solving
0 = -3 + -4z + 7z2

Solving for variable 'z'.

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

Reorder the terms:
3 + 4z + -7z2 = -3 + 3 + -4z + 4z + 7z2 + -7z2

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

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

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

Factor a trinomial.
(1 + -1z)(3 + 7z) = 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 '(3 + 7z)' equal to zero and attempt to solve:

Simplifying
3 + 7z = 0

Solving
3 + 7z = 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 + 7z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7z = 0 + -3
7z = 0 + -3

Combine like terms: 0 + -3 = -3
7z = -3

Divide each side by '7'.
z = -0.4285714286

Simplifying
z = -0.4285714286
Solution
z = {1, -0.4285714286}