(9-z)(4z+7)=0

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Solution for (9-z)(4z+7)=0 equation:


Simplifying
(9 + -1z)(4z + 7) = 0

Reorder the terms:
(9 + -1z)(7 + 4z) = 0

Multiply (9 + -1z) * (7 + 4z)
(9(7 + 4z) + -1z * (7 + 4z)) = 0
((7 * 9 + 4z * 9) + -1z * (7 + 4z)) = 0
((63 + 36z) + -1z * (7 + 4z)) = 0
(63 + 36z + (7 * -1z + 4z * -1z)) = 0
(63 + 36z + (-7z + -4z2)) = 0

Combine like terms: 36z + -7z = 29z
(63 + 29z + -4z2) = 0

Solving
63 + 29z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(9 + -1z)(7 + 4z) = 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 + 4z)' equal to zero and attempt to solve: Simplifying 7 + 4z = 0 Solving 7 + 4z = 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 + 4z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4z = 0 + -7 4z = 0 + -7 Combine like terms: 0 + -7 = -7 4z = -7 Divide each side by '4'. z = -1.75 Simplifying z = -1.75

Solution

z = {9, -1.75}

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