(1+z)(4z-6)=0

Solution for (1+z)(4z-6)=0 equation:

Simplifying
(1 + z)(4z + -6) = 0

Reorder the terms:
(1 + z)(-6 + 4z) = 0

Multiply (1 + z) * (-6 + 4z)
(1(-6 + 4z) + z(-6 + 4z)) = 0
((-6 * 1 + 4z * 1) + z(-6 + 4z)) = 0
((-6 + 4z) + z(-6 + 4z)) = 0
(-6 + 4z + (-6 * z + 4z * z)) = 0
(-6 + 4z + (-6z + 4z2)) = 0

Combine like terms: 4z + -6z = -2z
(-6 + -2z + 4z2) = 0

Solving
-6 + -2z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1z + 2z2) = 0

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

Ignore the factor 2.
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 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 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 + -2z = 0 + -3

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

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

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {-1, 1.5}