-5z(z-2)(z-7)=0

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Solution for -5z(z-2)(z-7)=0 equation: 


Simplifying
-5z(z + -2)(z + -7) = 0

Reorder the terms:
-5z(-2 + z)(z + -7) = 0

Reorder the terms:
-5z(-2 + z)(-7 + z) = 0

Multiply (-2 + z) * (-7 + z)
-5z(-2(-7 + z) + z(-7 + z)) = 0
-5z((-7 * -2 + z * -2) + z(-7 + z)) = 0
-5z((14 + -2z) + z(-7 + z)) = 0
-5z(14 + -2z + (-7 * z + z * z)) = 0
-5z(14 + -2z + (-7z + z2)) = 0

Combine like terms: -2z + -7z = -9z
-5z(14 + -9z + z2) = 0
(14 * -5z + -9z * -5z + z2 * -5z) = 0
(-70z + 45z2 + -5z3) = 0

Solving
-70z + 45z2 + -5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5z'.
5z(-14 + 9z + -1z2) = 0

Factor a trinomial.
5z((-7 + z)(2 + -1z)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0

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

Simplifying
-7 + z = 0

Solving
-7 + z = 0

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

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

Combine like terms: -7 + 7 = 0
0 + z = 0 + 7
z = 0 + 7

Combine like terms: 0 + 7 = 7
z = 7

Simplifying
z = 7

Subproblem 3
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
Solution
z = {0, 7, 2}

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