(3+z)(4z-7)=0

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Solution for (3+z)(4z-7)=0 equation:


Simplifying
(3 + z)(4z + -7) = 0

Reorder the terms:
(3 + z)(-7 + 4z) = 0

Multiply (3 + z) * (-7 + 4z)
(3(-7 + 4z) + z(-7 + 4z)) = 0
((-7 * 3 + 4z * 3) + z(-7 + 4z)) = 0
((-21 + 12z) + z(-7 + 4z)) = 0
(-21 + 12z + (-7 * z + 4z * z)) = 0
(-21 + 12z + (-7z + 4z2)) = 0

Combine like terms: 12z + -7z = 5z
(-21 + 5z + 4z2) = 0

Solving
-21 + 5z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(7 + -4z) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -4z)' equal to zero and attempt to solve: Simplifying 7 + -4z = 0 Solving 7 + -4z = 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 + -4z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4z = 0 + -7 -4z = 0 + -7 Combine like terms: 0 + -7 = -7 -4z = -7 Divide each side by '-4'. z = 1.75 Simplifying z = 1.75

Solution

z = {-3, 1.75}

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