(5y-4z)(7y+3z)=

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Solution for (5y-4z)(7y+3z)= equation: 


Simplifying
(5y + -4z)(7y + 3z) = 0

Multiply (5y + -4z) * (7y + 3z)
(5y * (7y + 3z) + -4z * (7y + 3z)) = 0
((7y * 5y + 3z * 5y) + -4z * (7y + 3z)) = 0

Reorder the terms:
((15yz + 35y2) + -4z * (7y + 3z)) = 0
((15yz + 35y2) + -4z * (7y + 3z)) = 0
(15yz + 35y2 + (7y * -4z + 3z * -4z)) = 0
(15yz + 35y2 + (-28yz + -12z2)) = 0

Reorder the terms:
(15yz + -28yz + 35y2 + -12z2) = 0

Combine like terms: 15yz + -28yz = -13yz
(-13yz + 35y2 + -12z2) = 0

Solving
-13yz + 35y2 + -12z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5y + -4z)(7y + 3z) = 0


Subproblem 1
Set the factor '(5y + -4z)' equal to zero and attempt to solve:

Simplifying
5y + -4z = 0

Solving
5y + -4z = 0

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

Add '4z' to each side of the equation.
5y + -4z + 4z = 0 + 4z

Combine like terms: -4z + 4z = 0
5y + 0 = 0 + 4z
5y = 0 + 4z
Remove the zero:
5y = 4z

Divide each side by '5'.
y = 0.8z

Simplifying
y = 0.8z

Subproblem 2
Set the factor '(7y + 3z)' equal to zero and attempt to solve:

Simplifying
7y + 3z = 0

Solving
7y + 3z = 0

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

Add '-3z' to each side of the equation.
7y + 3z + -3z = 0 + -3z

Combine like terms: 3z + -3z = 0
7y + 0 = 0 + -3z
7y = 0 + -3z
Remove the zero:
7y = -3z

Divide each side by '7'.
y = -0.4285714286z

Simplifying
y = -0.4285714286z
Solution
y = {0.8z, -0.4285714286z}

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