(2z-7)(9+z)=0

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Solution for (2z-7)(9+z)=0 equation:


Simplifying
(2z + -7)(9 + z) = 0

Reorder the terms:
(-7 + 2z)(9 + z) = 0

Multiply (-7 + 2z) * (9 + z)
(-7(9 + z) + 2z * (9 + z)) = 0
((9 * -7 + z * -7) + 2z * (9 + z)) = 0
((-63 + -7z) + 2z * (9 + z)) = 0
(-63 + -7z + (9 * 2z + z * 2z)) = 0
(-63 + -7z + (18z + 2z2)) = 0

Combine like terms: -7z + 18z = 11z
(-63 + 11z + 2z2) = 0

Solving
-63 + 11z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + -1z)(7 + -2z) = 0

Subproblem 1

Set the factor '(-9 + -1z)' equal to zero and attempt to solve: Simplifying -9 + -1z = 0 Solving -9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1z = 0 + 9 -1z = 0 + 9 Combine like terms: 0 + 9 = 9 -1z = 9 Divide each side by '-1'. z = -9 Simplifying z = -9

Subproblem 2

Set the factor '(7 + -2z)' equal to zero and attempt to solve: Simplifying 7 + -2z = 0 Solving 7 + -2z = 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 + -2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2z = 0 + -7 -2z = 0 + -7 Combine like terms: 0 + -7 = -7 -2z = -7 Divide each side by '-2'. z = 3.5 Simplifying z = 3.5

Solution

z = {-9, 3.5}

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