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

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


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

Multiply (4y + -3z) * (y + 6z)
(4y * (y + 6z) + -3z * (y + 6z)) = 0
((y * 4y + 6z * 4y) + -3z * (y + 6z)) = 0

Reorder the terms:
((24yz + 4y2) + -3z * (y + 6z)) = 0
((24yz + 4y2) + -3z * (y + 6z)) = 0
(24yz + 4y2 + (y * -3z + 6z * -3z)) = 0
(24yz + 4y2 + (-3yz + -18z2)) = 0

Reorder the terms:
(24yz + -3yz + 4y2 + -18z2) = 0

Combine like terms: 24yz + -3yz = 21yz
(21yz + 4y2 + -18z2) = 0

Solving
21yz + 4y2 + -18z2 = 0

Solving for variable 'y'.

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


Subproblem 1
Set the factor '(4y + -3z)' equal to zero and attempt to solve:

Simplifying
4y + -3z = 0

Solving
4y + -3z = 0

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

Add '3z' to each side of the equation.
4y + -3z + 3z = 0 + 3z

Combine like terms: -3z + 3z = 0
4y + 0 = 0 + 3z
4y = 0 + 3z
Remove the zero:
4y = 3z

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

Simplifying
y = 0.75z

Subproblem 2
Set the factor '(y + 6z)' equal to zero and attempt to solve:

Simplifying
y + 6z = 0

Solving
y + 6z = 0

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

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

Combine like terms: 6z + -6z = 0
y + 0 = 0 + -6z
y = 0 + -6z
Remove the zero:
y = -6z

Simplifying
y = -6z
Solution
y = {0.75z, -6z}

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