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

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


Simplifying
(4 + -1z)(3z + -7) = 0

Reorder the terms:
(4 + -1z)(-7 + 3z) = 0

Multiply (4 + -1z) * (-7 + 3z)
(4(-7 + 3z) + -1z * (-7 + 3z)) = 0
((-7 * 4 + 3z * 4) + -1z * (-7 + 3z)) = 0
((-28 + 12z) + -1z * (-7 + 3z)) = 0
(-28 + 12z + (-7 * -1z + 3z * -1z)) = 0
(-28 + 12z + (7z + -3z2)) = 0

Combine like terms: 12z + 7z = 19z
(-28 + 19z + -3z2) = 0

Solving
-28 + 19z + -3z2 = 0

Solving for variable 'z'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -3z)' equal to zero and attempt to solve: Simplifying 7 + -3z = 0 Solving 7 + -3z = 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 + -3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3z = 0 + -7 -3z = 0 + -7 Combine like terms: 0 + -7 = -7 -3z = -7 Divide each side by '-3'. z = 2.333333333 Simplifying z = 2.333333333

Solution

z = {4, 2.333333333}

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