2z(2z+13)=14

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Solution for 2z(2z+13)=14 equation:


Simplifying
2z(2z + 13) = 14

Reorder the terms:
2z(13 + 2z) = 14
(13 * 2z + 2z * 2z) = 14
(26z + 4z2) = 14

Solving
26z + 4z2 = 14

Solving for variable 'z'.

Reorder the terms:
-14 + 26z + 4z2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 26z + 4z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 13z + 2z2) = 0

Factor a trinomial.
2((-7 + -1z)(1 + -2z)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-7 + -1z)' equal to zero and attempt to solve: Simplifying -7 + -1z = 0 Solving -7 + -1z = 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 + -1z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1z = 0 + 7 -1z = 0 + 7 Combine like terms: 0 + 7 = 7 -1z = 7 Divide each side by '-1'. z = -7 Simplifying z = -7

Subproblem 2

Set the factor '(1 + -2z)' equal to zero and attempt to solve: Simplifying 1 + -2z = 0 Solving 1 + -2z = 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 + -2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z = 0 + -1 -2z = 0 + -1 Combine like terms: 0 + -1 = -1 -2z = -1 Divide each side by '-2'. z = 0.5 Simplifying z = 0.5

Solution

z = {-7, 0.5}

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