(2-z)(4z-7)=0

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Solution for (2-z)(4z-7)=0 equation:


Simplifying
(2 + -1z)(4z + -7) = 0

Reorder the terms:
(2 + -1z)(-7 + 4z) = 0

Multiply (2 + -1z) * (-7 + 4z)
(2(-7 + 4z) + -1z * (-7 + 4z)) = 0
((-7 * 2 + 4z * 2) + -1z * (-7 + 4z)) = 0
((-14 + 8z) + -1z * (-7 + 4z)) = 0
(-14 + 8z + (-7 * -1z + 4z * -1z)) = 0
(-14 + 8z + (7z + -4z2)) = 0

Combine like terms: 8z + 7z = 15z
(-14 + 15z + -4z2) = 0

Solving
-14 + 15z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + z)(7 + -4z) = 0

Subproblem 1

Set the factor '(-2 + z)' equal to zero and attempt to solve: Simplifying -2 + z = 0 Solving -2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + z = 0 + 2 z = 0 + 2 Combine like terms: 0 + 2 = 2 z = 2 Simplifying z = 2

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 = {2, 1.75}

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