(3+z)(3z+7)=0

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Solution for (3+z)(3z+7)=0 equation:


Simplifying
(3 + z)(3z + 7) = 0

Reorder the terms:
(3 + z)(7 + 3z) = 0

Multiply (3 + z) * (7 + 3z)
(3(7 + 3z) + z(7 + 3z)) = 0
((7 * 3 + 3z * 3) + z(7 + 3z)) = 0
((21 + 9z) + z(7 + 3z)) = 0
(21 + 9z + (7 * z + 3z * z)) = 0
(21 + 9z + (7z + 3z2)) = 0

Combine like terms: 9z + 7z = 16z
(21 + 16z + 3z2) = 0

Solving
21 + 16z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(7 + 3z) = 0

Subproblem 1

Set the factor '(3 + z)' equal to zero and attempt to solve: Simplifying 3 + z = 0 Solving 3 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z = 0 + -3 z = 0 + -3 Combine like terms: 0 + -3 = -3 z = -3 Simplifying z = -3

Subproblem 2

Set the factor '(7 + 3z)' equal to zero and attempt to solve: Simplifying 7 + 3z = 0 Solving 7 + 3z = 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 + 3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3z = 0 + -7 3z = 0 + -7 Combine like terms: 0 + -7 = -7 3z = -7 Divide each side by '3'. z = -2.333333333 Simplifying z = -2.333333333

Solution

z = {-3, -2.333333333}

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