30a^2-82a+56=0

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Solution for 30a^2-82a+56=0 equation:


Simplifying
30a2 + -82a + 56 = 0

Reorder the terms:
56 + -82a + 30a2 = 0

Solving
56 + -82a + 30a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -41a + 15a2) = 0

Factor a trinomial.
2((4 + -3a)(7 + -5a)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333

Subproblem 2

Set the factor '(7 + -5a)' equal to zero and attempt to solve: Simplifying 7 + -5a = 0 Solving 7 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5a = 0 + -7 -5a = 0 + -7 Combine like terms: 0 + -7 = -7 -5a = -7 Divide each side by '-5'. a = 1.4 Simplifying a = 1.4

Solution

a = {1.333333333, 1.4}

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