(4y+z)(2y+3z)=

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Solution for (4y+z)(2y+3z)= equation: 


Simplifying
(4y + z)(2y + 3z) = 0

Multiply (4y + z) * (2y + 3z)
(4y * (2y + 3z) + z(2y + 3z)) = 0
((2y * 4y + 3z * 4y) + z(2y + 3z)) = 0

Reorder the terms:
((12yz + 8y2) + z(2y + 3z)) = 0
((12yz + 8y2) + z(2y + 3z)) = 0
(12yz + 8y2 + (2y * z + 3z * z)) = 0
(12yz + 8y2 + (2yz + 3z2)) = 0

Reorder the terms:
(12yz + 2yz + 8y2 + 3z2) = 0

Combine like terms: 12yz + 2yz = 14yz
(14yz + 8y2 + 3z2) = 0

Solving
14yz + 8y2 + 3z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(4y + z)(2y + 3z) = 0


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

Simplifying
4y + z = 0

Solving
4y + z = 0

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

Add '-1z' to each side of the equation.
4y + z + -1z = 0 + -1z

Combine like terms: z + -1z = 0
4y + 0 = 0 + -1z
4y = 0 + -1z
Remove the zero:
4y = -1z

Divide each side by '4'.
y = -0.25z

Simplifying
y = -0.25z

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

Simplifying
2y + 3z = 0

Solving
2y + 3z = 0

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

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

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

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

Simplifying
y = -1.5z
Solution
y = {-0.25z, -1.5z}

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