=16z^2-16z+3

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Solution for =16z^2-16z+3 equation:


Simplifying
0 = 16z2 + -16z + 3

Reorder the terms:
0 = 3 + -16z + 16z2

Solving
0 = 3 + -16z + 16z2

Solving for variable 'z'.

Combine like terms: 0 + -3 = -3
-3 + 16z + -16z2 = 3 + -16z + 16z2 + -3 + 16z + -16z2

Reorder the terms:
-3 + 16z + -16z2 = 3 + -3 + -16z + 16z + 16z2 + -16z2

Combine like terms: 3 + -3 = 0
-3 + 16z + -16z2 = 0 + -16z + 16z + 16z2 + -16z2
-3 + 16z + -16z2 = -16z + 16z + 16z2 + -16z2

Combine like terms: -16z + 16z = 0
-3 + 16z + -16z2 = 0 + 16z2 + -16z2
-3 + 16z + -16z2 = 16z2 + -16z2

Combine like terms: 16z2 + -16z2 = 0
-3 + 16z + -16z2 = 0

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

Subproblem 1

Set the factor '(-3 + 4z)' equal to zero and attempt to solve: Simplifying -3 + 4z = 0 Solving -3 + 4z = 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 + 4z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4z = 0 + 3 4z = 0 + 3 Combine like terms: 0 + 3 = 3 4z = 3 Divide each side by '4'. z = 0.75 Simplifying z = 0.75

Subproblem 2

Set the factor '(1 + -4z)' equal to zero and attempt to solve: Simplifying 1 + -4z = 0 Solving 1 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4z = 0 + -1 -4z = 0 + -1 Combine like terms: 0 + -1 = -1 -4z = -1 Divide each side by '-4'. z = 0.25 Simplifying z = 0.25

Solution

z = {0.75, 0.25}

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