3(a-4)2(a-1)=10-5a

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Solution for 3(a-4)2(a-1)=10-5a equation: 


Simplifying
3(a + -4) * 2(a + -1) = 10 + -5a

Reorder the terms:
3(-4 + a) * 2(a + -1) = 10 + -5a

Reorder the terms:
3(-4 + a) * 2(-1 + a) = 10 + -5a

Reorder the terms for easier multiplication:
3 * 2(-4 + a)(-1 + a) = 10 + -5a

Multiply 3 * 2
6(-4 + a)(-1 + a) = 10 + -5a

Multiply (-4 + a) * (-1 + a)
6(-4(-1 + a) + a(-1 + a)) = 10 + -5a
6((-1 * -4 + a * -4) + a(-1 + a)) = 10 + -5a
6((4 + -4a) + a(-1 + a)) = 10 + -5a
6(4 + -4a + (-1 * a + a * a)) = 10 + -5a
6(4 + -4a + (-1a + a2)) = 10 + -5a

Combine like terms: -4a + -1a = -5a
6(4 + -5a + a2) = 10 + -5a
(4 * 6 + -5a * 6 + a2 * 6) = 10 + -5a
(24 + -30a + 6a2) = 10 + -5a

Solving
24 + -30a + 6a2 = 10 + -5a

Solving for variable 'a'.

Reorder the terms:
24 + -10 + -30a + 5a + 6a2 = 10 + -5a + -10 + 5a

Combine like terms: 24 + -10 = 14
14 + -30a + 5a + 6a2 = 10 + -5a + -10 + 5a

Combine like terms: -30a + 5a = -25a
14 + -25a + 6a2 = 10 + -5a + -10 + 5a

Reorder the terms:
14 + -25a + 6a2 = 10 + -10 + -5a + 5a

Combine like terms: 10 + -10 = 0
14 + -25a + 6a2 = 0 + -5a + 5a
14 + -25a + 6a2 = -5a + 5a

Combine like terms: -5a + 5a = 0
14 + -25a + 6a2 = 0

Factor a trinomial.
(2 + -3a)(7 + -2a) = 0


Subproblem 1
Set the factor '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3a = 0 + -2
-3a = 0 + -2

Combine like terms: 0 + -2 = -2
-3a = -2

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667

Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve:

Simplifying
7 + -2a = 0

Solving
7 + -2a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2a = 0 + -7
-2a = 0 + -7

Combine like terms: 0 + -7 = -7
-2a = -7

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {0.6666666667, 3.5}

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