6a^2-34a+36=-4

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Solution for 6a^2-34a+36=-4 equation:


Simplifying
6a2 + -34a + 36 = -4

Reorder the terms:
36 + -34a + 6a2 = -4

Solving
36 + -34a + 6a2 = -4

Solving for variable 'a'.

Reorder the terms:
36 + 4 + -34a + 6a2 = -4 + 4

Combine like terms: 36 + 4 = 40
40 + -34a + 6a2 = -4 + 4

Combine like terms: -4 + 4 = 0
40 + -34a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -17a + 3a2) = 0

Factor a trinomial.
2((5 + -3a)(4 + -1a)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667

Subproblem 2

Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 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 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4

Solution

a = {1.666666667, 4}

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