(7z-u)(2z+3u)=

Solution for (7z-u)(2z+3u)= equation:

Simplifying
(7z + -1u)(2z + 3u) = 0

Reorder the terms:
(-1u + 7z)(2z + 3u) = 0

Reorder the terms:
(-1u + 7z)(3u + 2z) = 0

Multiply (-1u + 7z) * (3u + 2z)
(-1u * (3u + 2z) + 7z * (3u + 2z)) = 0
((3u * -1u + 2z * -1u) + 7z * (3u + 2z)) = 0

Reorder the terms:
((-2uz + -3u2) + 7z * (3u + 2z)) = 0
((-2uz + -3u2) + 7z * (3u + 2z)) = 0
(-2uz + -3u2 + (3u * 7z + 2z * 7z)) = 0
(-2uz + -3u2 + (21uz + 14z2)) = 0

Reorder the terms:
(-2uz + 21uz + -3u2 + 14z2) = 0

Combine like terms: -2uz + 21uz = 19uz
(19uz + -3u2 + 14z2) = 0

Solving
19uz + -3u2 + 14z2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3u + -2z)(u + -7z) = 0

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

Simplifying
-3u + -2z = 0

Solving
-3u + -2z = 0

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

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

Combine like terms: -2z + 2z = 0
-3u + 0 = 0 + 2z
-3u = 0 + 2z
Remove the zero:
-3u = 2z

Divide each side by '-3'.
u = -0.6666666667z

Simplifying
u = -0.6666666667z
Subproblem 2
Set the factor '(u + -7z)' equal to zero and attempt to solve:

Simplifying
u + -7z = 0

Solving
u + -7z = 0

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

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

Combine like terms: -7z + 7z = 0
u + 0 = 0 + 7z
u = 0 + 7z
Remove the zero:
u = 7z

Simplifying
u = 7z
Solution
u = {-0.6666666667z, 7z}