12z^2+16z-28=0

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Solution for 12z^2+16z-28=0 equation:


Simplifying
12z2 + 16z + -28 = 0

Reorder the terms:
-28 + 16z + 12z2 = 0

Solving
-28 + 16z + 12z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + 4z + 3z2) = 0

Factor a trinomial.
4((-7 + -3z)(1 + -1z)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

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

Solution

z = {-2.333333333, 1}

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