6a^2-17a=-12

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Solution for 6a^2-17a=-12 equation:


Simplifying
6a2 + -17a = -12

Reorder the terms:
-17a + 6a2 = -12

Solving
-17a + 6a2 = -12

Solving for variable 'a'.

Reorder the terms:
12 + -17a + 6a2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + -17a + 6a2 = 0

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

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 '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5

Solution

a = {1.333333333, 1.5}

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