(8z-4)(5z+10)=0

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Solution for (8z-4)(5z+10)=0 equation: 


Simplifying
(8z + -4)(5z + 10) = 0

Reorder the terms:
(-4 + 8z)(5z + 10) = 0

Reorder the terms:
(-4 + 8z)(10 + 5z) = 0

Multiply (-4 + 8z) * (10 + 5z)
(-4(10 + 5z) + 8z * (10 + 5z)) = 0
((10 * -4 + 5z * -4) + 8z * (10 + 5z)) = 0
((-40 + -20z) + 8z * (10 + 5z)) = 0
(-40 + -20z + (10 * 8z + 5z * 8z)) = 0
(-40 + -20z + (80z + 40z2)) = 0

Combine like terms: -20z + 80z = 60z
(-40 + 60z + 40z2) = 0

Solving
-40 + 60z + 40z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-2 + 3z + 2z2) = 0

Factor a trinomial.
20((-2 + -1z)(1 + -2z)) = 0

Ignore the factor 20.

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

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1z = 0 + 2
-1z = 0 + 2

Combine like terms: 0 + 2 = 2
-1z = 2

Divide each side by '-1'.
z = -2

Simplifying
z = -2

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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-2, 0.5}

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