=(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 = -45yz
0 = (-45yz + 25y2 + 8z2)

Solving
0 = -45yz + 25y2 + 8z2

Solving for variable 'y'.
Remove the zero:
45yz + -25y2 + -8z2 = -45yz + 25y2 + 8z2 + 45yz + -25y2 + -8z2

Reorder the terms:
45yz + -25y2 + -8z2 = -45yz + 45yz + 25y2 + -25y2 + 8z2 + -8z2

Combine like terms: -45yz + 45yz = 0
45yz + -25y2 + -8z2 = 0 + 25y2 + -25y2 + 8z2 + -8z2
45yz + -25y2 + -8z2 = 25y2 + -25y2 + 8z2 + -8z2

Combine like terms: 25y2 + -25y2 = 0
45yz + -25y2 + -8z2 = 0 + 8z2 + -8z2
45yz + -25y2 + -8z2 = 8z2 + -8z2

Combine like terms: 8z2 + -8z2 = 0
45yz + -25y2 + -8z2 = 0

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


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

Simplifying
-5y + z = 0

Solving
-5y + z = 0

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

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

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

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

Simplifying
y = 0.2z

Subproblem 2
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
Solution
y = {0.2z, 1.6z}

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