70z^2=5z+15

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Solution for 70z^2=5z+15 equation:


Simplifying
70z2 = 5z + 15

Reorder the terms:
70z2 = 15 + 5z

Solving
70z2 = 15 + 5z

Solving for variable 'z'.

Reorder the terms:
-15 + -5z + 70z2 = 15 + 5z + -15 + -5z

Reorder the terms:
-15 + -5z + 70z2 = 15 + -15 + 5z + -5z

Combine like terms: 15 + -15 = 0
-15 + -5z + 70z2 = 0 + 5z + -5z
-15 + -5z + 70z2 = 5z + -5z

Combine like terms: 5z + -5z = 0
-15 + -5z + 70z2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -1z + 14z2) = 0

Factor a trinomial.
5((-3 + -7z)(1 + -2z)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-3 + -7z)' equal to zero and attempt to solve: Simplifying -3 + -7z = 0 Solving -3 + -7z = 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 + -7z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7z = 0 + 3 -7z = 0 + 3 Combine like terms: 0 + 3 = 3 -7z = 3 Divide each side by '-7'. z = -0.4285714286 Simplifying z = -0.4285714286

Subproblem 2

Set the factor '(1 + -2z)' equal to zero and attempt to solve: Simplifying 1 + -2z = 0 Solving 1 + -2z = 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 + -2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z = 0 + -1 -2z = 0 + -1 Combine like terms: 0 + -1 = -1 -2z = -1 Divide each side by '-2'. z = 0.5 Simplifying z = 0.5

Solution

z = {-0.4285714286, 0.5}

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