(3z+2)(2z-11)=0

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Solution for (3z+2)(2z-11)=0 equation:


Simplifying
(3z + 2)(2z + -11) = 0

Reorder the terms:
(2 + 3z)(2z + -11) = 0

Reorder the terms:
(2 + 3z)(-11 + 2z) = 0

Multiply (2 + 3z) * (-11 + 2z)
(2(-11 + 2z) + 3z * (-11 + 2z)) = 0
((-11 * 2 + 2z * 2) + 3z * (-11 + 2z)) = 0
((-22 + 4z) + 3z * (-11 + 2z)) = 0
(-22 + 4z + (-11 * 3z + 2z * 3z)) = 0
(-22 + 4z + (-33z + 6z2)) = 0

Combine like terms: 4z + -33z = -29z
(-22 + -29z + 6z2) = 0

Solving
-22 + -29z + 6z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -3z)(11 + -2z) = 0

Subproblem 1

Set the factor '(-2 + -3z)' equal to zero and attempt to solve: Simplifying -2 + -3z = 0 Solving -2 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3z = 0 + 2 -3z = 0 + 2 Combine like terms: 0 + 2 = 2 -3z = 2 Divide each side by '-3'. z = -0.6666666667 Simplifying z = -0.6666666667

Subproblem 2

Set the factor '(11 + -2z)' equal to zero and attempt to solve: Simplifying 11 + -2z = 0 Solving 11 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2z = 0 + -11 -2z = 0 + -11 Combine like terms: 0 + -11 = -11 -2z = -11 Divide each side by '-2'. z = 5.5 Simplifying z = 5.5

Solution

z = {-0.6666666667, 5.5}

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