2z=21z^2-3

Solution for 2z=21z^2-3 equation:

Simplifying
2z = 21z2 + -3

Reorder the terms:
2z = -3 + 21z2

Solving
2z = -3 + 21z2

Solving for variable 'z'.

Reorder the terms:
3 + 2z + -21z2 = -3 + 21z2 + 3 + -21z2

Reorder the terms:
3 + 2z + -21z2 = -3 + 3 + 21z2 + -21z2

Combine like terms: -3 + 3 = 0
3 + 2z + -21z2 = 0 + 21z2 + -21z2
3 + 2z + -21z2 = 21z2 + -21z2

Combine like terms: 21z2 + -21z2 = 0
3 + 2z + -21z2 = 0

Factor a trinomial.
(3 + -7z)(1 + 3z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 3z)' equal to zero and attempt to solve:

Simplifying
1 + 3z = 0

Solving
1 + 3z = 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 + 3z = 0 + -1

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

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

Divide each side by '3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Solution
z = {0.4285714286, -0.3333333333}