10a-(4(5a-3(a-1)-3(4a-3a+1)))=5a-15

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Solution for 10a-(4(5a-3(a-1)-3(4a-3a+1)))=5a-15 equation: 


Simplifying
10a + -1(4(5a + -3(a + -1) + -3(4a + -3a + 1))) = 5a + -15

Reorder the terms:
10a + -1(4(5a + -3(-1 + a) + -3(4a + -3a + 1))) = 5a + -15
10a + -1(4(5a + (-1 * -3 + a * -3) + -3(4a + -3a + 1))) = 5a + -15
10a + -1(4(5a + (3 + -3a) + -3(4a + -3a + 1))) = 5a + -15

Reorder the terms:
10a + -1(4(5a + 3 + -3a + -3(1 + 4a + -3a))) = 5a + -15

Combine like terms: 4a + -3a = 1a
10a + -1(4(5a + 3 + -3a + -3(1 + 1a))) = 5a + -15
10a + -1(4(5a + 3 + -3a + (1 * -3 + 1a * -3))) = 5a + -15
10a + -1(4(5a + 3 + -3a + (-3 + -3a))) = 5a + -15

Reorder the terms:
10a + -1(4(3 + -3 + 5a + -3a + -3a)) = 5a + -15

Combine like terms: 3 + -3 = 0
10a + -1(4(0 + 5a + -3a + -3a)) = 5a + -15
10a + -1(4(5a + -3a + -3a)) = 5a + -15

Combine like terms: 5a + -3a = 2a
10a + -1(4(2a + -3a)) = 5a + -15

Combine like terms: 2a + -3a = -1a
10a + -1(4(-1a)) = 5a + -15

Remove parenthesis around (-1a)
10a + -1(4 * -1a) = 5a + -15

Multiply 4 * -1
10a + -1(-4a) = 5a + -15

Remove parenthesis around (-4a)
10a + -1 * -4a = 5a + -15

Multiply -1 * -4
10a + 4a = 5a + -15

Combine like terms: 10a + 4a = 14a
14a = 5a + -15

Reorder the terms:
14a = -15 + 5a

Solving
14a = -15 + 5a

Solving for variable 'a'.

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

Add '-5a' to each side of the equation.
14a + -5a = -15 + 5a + -5a

Combine like terms: 14a + -5a = 9a
9a = -15 + 5a + -5a

Combine like terms: 5a + -5a = 0
9a = -15 + 0
9a = -15

Divide each side by '9'.
a = -1.666666667

Simplifying
a = -1.666666667

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