2z(3z+1)=-9z-3

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Solution for 2z(3z+1)=-9z-3 equation:


Simplifying
2z(3z + 1) = -9z + -3

Reorder the terms:
2z(1 + 3z) = -9z + -3
(1 * 2z + 3z * 2z) = -9z + -3
(2z + 6z2) = -9z + -3

Reorder the terms:
2z + 6z2 = -3 + -9z

Solving
2z + 6z2 = -3 + -9z

Solving for variable 'z'.

Reorder the terms:
3 + 2z + 9z + 6z2 = -3 + -9z + 3 + 9z

Combine like terms: 2z + 9z = 11z
3 + 11z + 6z2 = -3 + -9z + 3 + 9z

Reorder the terms:
3 + 11z + 6z2 = -3 + 3 + -9z + 9z

Combine like terms: -3 + 3 = 0
3 + 11z + 6z2 = 0 + -9z + 9z
3 + 11z + 6z2 = -9z + 9z

Combine like terms: -9z + 9z = 0
3 + 11z + 6z2 = 0

Factor a trinomial.
(3 + 2z)(1 + 3z) = 0

Subproblem 1

Set the factor '(3 + 2z)' equal to zero and attempt to solve: Simplifying 3 + 2z = 0 Solving 3 + 2z = 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 + 2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2z = 0 + -3 2z = 0 + -3 Combine like terms: 0 + -3 = -3 2z = -3 Divide each side by '2'. z = -1.5 Simplifying z = -1.5

Subproblem 2

Set the factor '(1 + 3z)' equal to zero and attempt to solve: Simplifying 1 + 3z = 0 Solving 1 + 3z = 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 + 3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3z = 0 + -1 3z = 0 + -1 Combine like terms: 0 + -1 = -1 3z = -1 Divide each side by '3'. z = -0.3333333333 Simplifying z = -0.3333333333

Solution

z = {-1.5, -0.3333333333}

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