(2z+1)(2z-5)=

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Solution for (2z+1)(2z-5)= equation:


Simplifying
(2z + 1)(2z + -5) = 0

Reorder the terms:
(1 + 2z)(2z + -5) = 0

Reorder the terms:
(1 + 2z)(-5 + 2z) = 0

Multiply (1 + 2z) * (-5 + 2z)
(1(-5 + 2z) + 2z * (-5 + 2z)) = 0
((-5 * 1 + 2z * 1) + 2z * (-5 + 2z)) = 0
((-5 + 2z) + 2z * (-5 + 2z)) = 0
(-5 + 2z + (-5 * 2z + 2z * 2z)) = 0
(-5 + 2z + (-10z + 4z2)) = 0

Combine like terms: 2z + -10z = -8z
(-5 + -8z + 4z2) = 0

Solving
-5 + -8z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -2z)(5 + -2z) = 0

Subproblem 1

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

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 = {-0.5, 2.5}

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