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

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


Simplifying
2(z + -5)(-1z + 7) = 0

Reorder the terms:
2(-5 + z)(-1z + 7) = 0

Reorder the terms:
2(-5 + z)(7 + -1z) = 0

Multiply (-5 + z) * (7 + -1z)
2(-5(7 + -1z) + z(7 + -1z)) = 0
2((7 * -5 + -1z * -5) + z(7 + -1z)) = 0
2((-35 + 5z) + z(7 + -1z)) = 0
2(-35 + 5z + (7 * z + -1z * z)) = 0
2(-35 + 5z + (7z + -1z2)) = 0

Combine like terms: 5z + 7z = 12z
2(-35 + 12z + -1z2) = 0
(-35 * 2 + 12z * 2 + -1z2 * 2) = 0
(-70 + 24z + -2z2) = 0

Solving
-70 + 24z + -2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 12z + -1z2) = 0

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

Ignore the factor 2.

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

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

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

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {7, 5}

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