(z+5)(z-7)=

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


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

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

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

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

Combine like terms: 5z + -7z = -2z
(-35 + -2z + z2) = 0

Solving
-35 + -2z + z2 = 0

Solving for variable 'z'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 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 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7

Solution

z = {-5, 7}

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