4z(2z+3)=36

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Solution for 4z(2z+3)=36 equation:


Simplifying
4z(2z + 3) = 36

Reorder the terms:
4z(3 + 2z) = 36
(3 * 4z + 2z * 4z) = 36
(12z + 8z2) = 36

Solving
12z + 8z2 = 36

Solving for variable 'z'.

Reorder the terms:
-36 + 12z + 8z2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 12z + 8z2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + 3z + 2z2) = 0

Factor a trinomial.
4((-3 + -1z)(3 + -2z)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

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

Solution

z = {-3, 1.5}

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