6z^2=5z+50

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Solution for 6z^2=5z+50 equation:


Simplifying
6z2 = 5z + 50

Reorder the terms:
6z2 = 50 + 5z

Solving
6z2 = 50 + 5z

Solving for variable 'z'.

Reorder the terms:
-50 + -5z + 6z2 = 50 + 5z + -50 + -5z

Reorder the terms:
-50 + -5z + 6z2 = 50 + -50 + 5z + -5z

Combine like terms: 50 + -50 = 0
-50 + -5z + 6z2 = 0 + 5z + -5z
-50 + -5z + 6z2 = 5z + -5z

Combine like terms: 5z + -5z = 0
-50 + -5z + 6z2 = 0

Factor a trinomial.
(-5 + -2z)(10 + -3z) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(10 + -3z)' equal to zero and attempt to solve: Simplifying 10 + -3z = 0 Solving 10 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3z = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3z = 0 + -10 -3z = 0 + -10 Combine like terms: 0 + -10 = -10 -3z = -10 Divide each side by '-3'. z = 3.333333333 Simplifying z = 3.333333333

Solution

z = {-2.5, 3.333333333}

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