5z^2+12z+7=0

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Solution for 5z^2+12z+7=0 equation:


Simplifying
5z2 + 12z + 7 = 0

Reorder the terms:
7 + 12z + 5z2 = 0

Solving
7 + 12z + 5z2 = 0

Solving for variable 'z'.

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

Subproblem 1

Set the factor '(7 + 5z)' equal to zero and attempt to solve: Simplifying 7 + 5z = 0 Solving 7 + 5z = 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 + 5z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5z = 0 + -7 5z = 0 + -7 Combine like terms: 0 + -7 = -7 5z = -7 Divide each side by '5'. z = -1.4 Simplifying z = -1.4

Subproblem 2

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

Solution

z = {-1.4, -1}

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