4(a^2-3a-4)-2(5a^2-a-6)=

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Solution for 4(a^2-3a-4)-2(5a^2-a-6)= equation: 


Simplifying
4(a2 + -3a + -4) + -2(5a2 + -1a + -6) = 0

Reorder the terms:
4(-4 + -3a + a2) + -2(5a2 + -1a + -6) = 0
(-4 * 4 + -3a * 4 + a2 * 4) + -2(5a2 + -1a + -6) = 0
(-16 + -12a + 4a2) + -2(5a2 + -1a + -6) = 0

Reorder the terms:
-16 + -12a + 4a2 + -2(-6 + -1a + 5a2) = 0
-16 + -12a + 4a2 + (-6 * -2 + -1a * -2 + 5a2 * -2) = 0
-16 + -12a + 4a2 + (12 + 2a + -10a2) = 0

Reorder the terms:
-16 + 12 + -12a + 2a + 4a2 + -10a2 = 0

Combine like terms: -16 + 12 = -4
-4 + -12a + 2a + 4a2 + -10a2 = 0

Combine like terms: -12a + 2a = -10a
-4 + -10a + 4a2 + -10a2 = 0

Combine like terms: 4a2 + -10a2 = -6a2
-4 + -10a + -6a2 = 0

Solving
-4 + -10a + -6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(2 + 5a + 3a2) = 0

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

Ignore the factor -2.

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

Simplifying
1 + a = 0

Solving
1 + a = 0

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

Add '-1' to each side of the equation.
1 + -1 + a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

Simplifying
a = -1

Subproblem 2
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
Solution
a = {-1, -0.6666666667}

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