9z^2+15z-4=3z-8

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Solution for 9z^2+15z-4=3z-8 equation:


Simplifying
9z2 + 15z + -4 = 3z + -8

Reorder the terms:
-4 + 15z + 9z2 = 3z + -8

Reorder the terms:
-4 + 15z + 9z2 = -8 + 3z

Solving
-4 + 15z + 9z2 = -8 + 3z

Solving for variable 'z'.

Reorder the terms:
-4 + 8 + 15z + -3z + 9z2 = -8 + 3z + 8 + -3z

Combine like terms: -4 + 8 = 4
4 + 15z + -3z + 9z2 = -8 + 3z + 8 + -3z

Combine like terms: 15z + -3z = 12z
4 + 12z + 9z2 = -8 + 3z + 8 + -3z

Reorder the terms:
4 + 12z + 9z2 = -8 + 8 + 3z + -3z

Combine like terms: -8 + 8 = 0
4 + 12z + 9z2 = 0 + 3z + -3z
4 + 12z + 9z2 = 3z + -3z

Combine like terms: 3z + -3z = 0
4 + 12z + 9z2 = 0

Factor a trinomial.
(2 + 3z)(2 + 3z) = 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 '(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

Solution

z = {-0.6666666667, -0.6666666667}

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