(5z^2-2+1)(3z^2+2-4)=

Solution for (5z^2-2+1)(3z^2+2-4)= equation:

Simplifying
(5z2 + -2 + 1)(3z2 + 2 + -4) = 0

Reorder the terms:
(-2 + 1 + 5z2)(3z2 + 2 + -4) = 0

Combine like terms: -2 + 1 = -1
(-1 + 5z2)(3z2 + 2 + -4) = 0

Reorder the terms:
(-1 + 5z2)(2 + -4 + 3z2) = 0

Combine like terms: 2 + -4 = -2
(-1 + 5z2)(-2 + 3z2) = 0

Multiply (-1 + 5z2) * (-2 + 3z2)
(-1(-2 + 3z2) + 5z2 * (-2 + 3z2)) = 0
((-2 * -1 + 3z2 * -1) + 5z2 * (-2 + 3z2)) = 0
((2 + -3z2) + 5z2 * (-2 + 3z2)) = 0
(2 + -3z2 + (-2 * 5z2 + 3z2 * 5z2)) = 0
(2 + -3z2 + (-10z2 + 15z4)) = 0

Combine like terms: -3z2 + -10z2 = -13z2
(2 + -13z2 + 15z4) = 0

Solving
2 + -13z2 + 15z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -5z2)(2 + -3z2) = 0

Subproblem 1
Set the factor '(1 + -5z2)' equal to zero and attempt to solve:

Simplifying
1 + -5z2 = 0

Solving
1 + -5z2 = 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 + -5z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5z2 = 0 + -1
-5z2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5z2 = -1

Divide each side by '-5'.
z2 = 0.2

Simplifying
z2 = 0.2

Take the square root of each side:
z = {-0.447213596, 0.447213596}
Subproblem 2
Set the factor '(2 + -3z2)' equal to zero and attempt to solve:

Simplifying
2 + -3z2 = 0

Solving
2 + -3z2 = 0

Move all terms containing z to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3z2 = 0 + -2

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

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

Divide each side by '-3'.
z2 = 0.6666666667

Simplifying
z2 = 0.6666666667

Take the square root of each side:
z = {-0.816496581, 0.816496581}
Solution
z = {-0.447213596, 0.447213596, -0.816496581, 0.816496581}