-6a(a-3)=-5(3a-1)-5

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Solution for -6a(a-3)=-5(3a-1)-5 equation:


Simplifying
-6a(a + -3) = -5(3a + -1) + -5

Reorder the terms:
-6a(-3 + a) = -5(3a + -1) + -5
(-3 * -6a + a * -6a) = -5(3a + -1) + -5
(18a + -6a2) = -5(3a + -1) + -5

Reorder the terms:
18a + -6a2 = -5(-1 + 3a) + -5
18a + -6a2 = (-1 * -5 + 3a * -5) + -5
18a + -6a2 = (5 + -15a) + -5

Reorder the terms:
18a + -6a2 = 5 + -5 + -15a

Combine like terms: 5 + -5 = 0
18a + -6a2 = 0 + -15a
18a + -6a2 = -15a

Solving
18a + -6a2 = -15a

Solving for variable 'a'.

Reorder the terms:
18a + 15a + -6a2 = -15a + 15a

Combine like terms: 18a + 15a = 33a
33a + -6a2 = -15a + 15a

Combine like terms: -15a + 15a = 0
33a + -6a2 = 0

Factor out the Greatest Common Factor (GCF), '3a'.
3a(11 + -2a) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0

Subproblem 2
Set the factor '(11 + -2a)' equal to zero and attempt to solve:

Simplifying
11 + -2a = 0

Solving
11 + -2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + -2a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2a = 0 + -11
-2a = 0 + -11

Combine like terms: 0 + -11 = -11
-2a = -11

Divide each side by '-2'.
a = 5.5

Simplifying
a = 5.5
Solution
a = {0, 5.5}

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