(4z-3)(7z+6)=

Solution for (4z-3)(7z+6)= equation:

Simplifying
(4z + -3)(7z + 6) = 0

Reorder the terms:
(-3 + 4z)(7z + 6) = 0

Reorder the terms:
(-3 + 4z)(6 + 7z) = 0

Multiply (-3 + 4z) * (6 + 7z)
(-3(6 + 7z) + 4z * (6 + 7z)) = 0
((6 * -3 + 7z * -3) + 4z * (6 + 7z)) = 0
((-18 + -21z) + 4z * (6 + 7z)) = 0
(-18 + -21z + (6 * 4z + 7z * 4z)) = 0
(-18 + -21z + (24z + 28z2)) = 0

Combine like terms: -21z + 24z = 3z
(-18 + 3z + 28z2) = 0

Solving
-18 + 3z + 28z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -7z)(3 + -4z) = 0

Subproblem 1
Set the factor '(-6 + -7z)' equal to zero and attempt to solve:

Simplifying
-6 + -7z = 0

Solving
-6 + -7z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -7z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7z = 0 + 6
-7z = 0 + 6

Combine like terms: 0 + 6 = 6
-7z = 6

Divide each side by '-7'.
z = -0.8571428571

Simplifying
z = -0.8571428571
Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

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

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

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

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {-0.8571428571, 0.75}