a(6a-13)=8

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Solution for a(6a-13)=8 equation:


Simplifying
a(6a + -13) = 8

Reorder the terms:
a(-13 + 6a) = 8
(-13 * a + 6a * a) = 8
(-13a + 6a2) = 8

Solving
-13a + 6a2 = 8

Solving for variable 'a'.

Reorder the terms:
-8 + -13a + 6a2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -13a + 6a2 = 0

Factor a trinomial.
(-1 + -2a)(8 + -3a) = 0

Subproblem 1

Set the factor '(-1 + -2a)' equal to zero and attempt to solve: Simplifying -1 + -2a = 0 Solving -1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2a = 0 + 1 -2a = 0 + 1 Combine like terms: 0 + 1 = 1 -2a = 1 Divide each side by '-2'. a = -0.5 Simplifying a = -0.5

Subproblem 2

Set the factor '(8 + -3a)' equal to zero and attempt to solve: Simplifying 8 + -3a = 0 Solving 8 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3a = 0 + -8 -3a = 0 + -8 Combine like terms: 0 + -8 = -8 -3a = -8 Divide each side by '-3'. a = 2.666666667 Simplifying a = 2.666666667

Solution

a = {-0.5, 2.666666667}

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