=(5y-z)(5y+8z)

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Solution for =(5y-z)(5y+8z) equation: 


Simplifying
0 = (5y + -1z)(5y + 8z)

Multiply (5y + -1z) * (5y + 8z)
0 = (5y * (5y + 8z) + -1z * (5y + 8z))
0 = ((5y * 5y + 8z * 5y) + -1z * (5y + 8z))

Reorder the terms:
0 = ((40yz + 25y2) + -1z * (5y + 8z))
0 = ((40yz + 25y2) + -1z * (5y + 8z))
0 = (40yz + 25y2 + (5y * -1z + 8z * -1z))
0 = (40yz + 25y2 + (-5yz + -8z2))

Reorder the terms:
0 = (40yz + -5yz + 25y2 + -8z2)

Combine like terms: 40yz + -5yz = 35yz
0 = (35yz + 25y2 + -8z2)

Solving
0 = 35yz + 25y2 + -8z2

Solving for variable 'y'.
Remove the zero:
-35yz + -25y2 + 8z2 = 35yz + 25y2 + -8z2 + -35yz + -25y2 + 8z2

Reorder the terms:
-35yz + -25y2 + 8z2 = 35yz + -35yz + 25y2 + -25y2 + -8z2 + 8z2

Combine like terms: 35yz + -35yz = 0
-35yz + -25y2 + 8z2 = 0 + 25y2 + -25y2 + -8z2 + 8z2
-35yz + -25y2 + 8z2 = 25y2 + -25y2 + -8z2 + 8z2

Combine like terms: 25y2 + -25y2 = 0
-35yz + -25y2 + 8z2 = 0 + -8z2 + 8z2
-35yz + -25y2 + 8z2 = -8z2 + 8z2

Combine like terms: -8z2 + 8z2 = 0
-35yz + -25y2 + 8z2 = 0

Factor a trinomial.
(-5y + -8z)(5y + -1z) = 0


Subproblem 1
Set the factor '(-5y + -8z)' equal to zero and attempt to solve:

Simplifying
-5y + -8z = 0

Solving
-5y + -8z = 0

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

Add '8z' to each side of the equation.
-5y + -8z + 8z = 0 + 8z

Combine like terms: -8z + 8z = 0
-5y + 0 = 0 + 8z
-5y = 0 + 8z
Remove the zero:
-5y = 8z

Divide each side by '-5'.
y = -1.6z

Simplifying
y = -1.6z

Subproblem 2
Set the factor '(5y + -1z)' equal to zero and attempt to solve:

Simplifying
5y + -1z = 0

Solving
5y + -1z = 0

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

Add 'z' to each side of the equation.
5y + -1z + z = 0 + z

Combine like terms: -1z + z = 0
5y + 0 = 0 + z
5y = 0 + z
Remove the zero:
5y = z

Divide each side by '5'.
y = 0.2z

Simplifying
y = 0.2z
Solution
y = {-1.6z, 0.2z}

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