3z(z-4)+8(z-4)=0

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Solution for 3z(z-4)+8(z-4)=0 equation:


Simplifying
3z(z + -4) + 8(z + -4) = 0

Reorder the terms:
3z(-4 + z) + 8(z + -4) = 0
(-4 * 3z + z * 3z) + 8(z + -4) = 0
(-12z + 3z2) + 8(z + -4) = 0

Reorder the terms:
-12z + 3z2 + 8(-4 + z) = 0
-12z + 3z2 + (-4 * 8 + z * 8) = 0
-12z + 3z2 + (-32 + 8z) = 0

Reorder the terms:
-32 + -12z + 8z + 3z2 = 0

Combine like terms: -12z + 8z = -4z
-32 + -4z + 3z2 = 0

Solving
-32 + -4z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + -3z)(4 + -1z) = 0

Subproblem 1

Set the factor '(-8 + -3z)' equal to zero and attempt to solve: Simplifying -8 + -3z = 0 Solving -8 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3z = 0 + 8 -3z = 0 + 8 Combine like terms: 0 + 8 = 8 -3z = 8 Divide each side by '-3'. z = -2.666666667 Simplifying z = -2.666666667

Subproblem 2

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

Solution

z = {-2.666666667, 4}

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