(3z+1)(4z+3)=0

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Solution for (3z+1)(4z+3)=0 equation:


Simplifying
(3z + 1)(4z + 3) = 0

Reorder the terms:
(1 + 3z)(4z + 3) = 0

Reorder the terms:
(1 + 3z)(3 + 4z) = 0

Multiply (1 + 3z) * (3 + 4z)
(1(3 + 4z) + 3z * (3 + 4z)) = 0
((3 * 1 + 4z * 1) + 3z * (3 + 4z)) = 0
((3 + 4z) + 3z * (3 + 4z)) = 0
(3 + 4z + (3 * 3z + 4z * 3z)) = 0
(3 + 4z + (9z + 12z2)) = 0

Combine like terms: 4z + 9z = 13z
(3 + 13z + 12z2) = 0

Solving
3 + 13z + 12z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + 4z)(1 + 3z) = 0

Subproblem 1

Set the factor '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 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 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75

Subproblem 2

Set the factor '(1 + 3z)' equal to zero and attempt to solve: Simplifying 1 + 3z = 0 Solving 1 + 3z = 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 + 3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3z = 0 + -1 3z = 0 + -1 Combine like terms: 0 + -1 = -1 3z = -1 Divide each side by '3'. z = -0.3333333333 Simplifying z = -0.3333333333

Solution

z = {-0.75, -0.3333333333}

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