4z^2-20z+28=3

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Solution for 4z^2-20z+28=3 equation:


Simplifying
4z2 + -20z + 28 = 3

Reorder the terms:
28 + -20z + 4z2 = 3

Solving
28 + -20z + 4z2 = 3

Solving for variable 'z'.

Reorder the terms:
28 + -3 + -20z + 4z2 = 3 + -3

Combine like terms: 28 + -3 = 25
25 + -20z + 4z2 = 3 + -3

Combine like terms: 3 + -3 = 0
25 + -20z + 4z2 = 0

Factor a trinomial.
(5 + -2z)(5 + -2z) = 0

Subproblem 1

Set the factor '(5 + -2z)' equal to zero and attempt to solve: Simplifying 5 + -2z = 0 Solving 5 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z = 0 + -5 -2z = 0 + -5 Combine like terms: 0 + -5 = -5 -2z = -5 Divide each side by '-2'. z = 2.5 Simplifying z = 2.5

Subproblem 2

Set the factor '(5 + -2z)' equal to zero and attempt to solve: Simplifying 5 + -2z = 0 Solving 5 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z = 0 + -5 -2z = 0 + -5 Combine like terms: 0 + -5 = -5 -2z = -5 Divide each side by '-2'. z = 2.5 Simplifying z = 2.5

Solution

z = {2.5, 2.5}

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