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

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


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

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

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

Combine like terms: 3z + -4z = -1z
(-4 + -1z + 3z2) = 0

Solving
-4 + -1z + 3z2 = 0

Solving for variable 'z'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -3z)' equal to zero and attempt to solve: Simplifying 4 + -3z = 0 Solving 4 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3z = 0 + -4 -3z = 0 + -4 Combine like terms: 0 + -4 = -4 -3z = -4 Divide each side by '-3'. z = 1.333333333 Simplifying z = 1.333333333

Solution

z = {-1, 1.333333333}

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