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

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


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

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

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

Multiply (-3 + 4z) * (4 + z)
(-3(4 + z) + 4z * (4 + z)) = 0
((4 * -3 + z * -3) + 4z * (4 + z)) = 0
((-12 + -3z) + 4z * (4 + z)) = 0
(-12 + -3z + (4 * 4z + z * 4z)) = 0
(-12 + -3z + (16z + 4z2)) = 0

Combine like terms: -3z + 16z = 13z
(-12 + 13z + 4z2) = 0

Solving
-12 + 13z + 4z2 = 0

Solving for variable 'z'.

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

Subproblem 1

Set the factor '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 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 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4

Subproblem 2

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

Solution

z = {-4, 0.75}

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