(7+z)(5z-4)=0

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Solution for (7+z)(5z-4)=0 equation:


Simplifying
(7 + z)(5z + -4) = 0

Reorder the terms:
(7 + z)(-4 + 5z) = 0

Multiply (7 + z) * (-4 + 5z)
(7(-4 + 5z) + z(-4 + 5z)) = 0
((-4 * 7 + 5z * 7) + z(-4 + 5z)) = 0
((-28 + 35z) + z(-4 + 5z)) = 0
(-28 + 35z + (-4 * z + 5z * z)) = 0
(-28 + 35z + (-4z + 5z2)) = 0

Combine like terms: 35z + -4z = 31z
(-28 + 31z + 5z2) = 0

Solving
-28 + 31z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -1z)(4 + -5z) = 0

Subproblem 1

Set the factor '(-7 + -1z)' equal to zero and attempt to solve: Simplifying -7 + -1z = 0 Solving -7 + -1z = 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 + -1z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1z = 0 + 7 -1z = 0 + 7 Combine like terms: 0 + 7 = 7 -1z = 7 Divide each side by '-1'. z = -7 Simplifying z = -7

Subproblem 2

Set the factor '(4 + -5z)' equal to zero and attempt to solve: Simplifying 4 + -5z = 0 Solving 4 + -5z = 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 + -5z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5z = 0 + -4 -5z = 0 + -4 Combine like terms: 0 + -4 = -4 -5z = -4 Divide each side by '-5'. z = 0.8 Simplifying z = 0.8

Solution

z = {-7, 0.8}

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