3a(2a+4b)+2a(a-7b)=

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Solution for 3a(2a+4b)+2a(a-7b)= equation:


Simplifying
3a(2a + 4b) + 2a(a + -7b) = 0
(2a * 3a + 4b * 3a) + 2a(a + -7b) = 0

Reorder the terms:
(12ab + 6a2) + 2a(a + -7b) = 0
(12ab + 6a2) + 2a(a + -7b) = 0
12ab + 6a2 + (a * 2a + -7b * 2a) = 0

Reorder the terms:
12ab + 6a2 + (-14ab + 2a2) = 0
12ab + 6a2 + (-14ab + 2a2) = 0

Reorder the terms:
12ab + -14ab + 6a2 + 2a2 = 0

Combine like terms: 12ab + -14ab = -2ab
-2ab + 6a2 + 2a2 = 0

Combine like terms: 6a2 + 2a2 = 8a2
-2ab + 8a2 = 0

Solving
-2ab + 8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(-1b + 4a) = 0

Ignore the factor 2.

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 '(-1b + 4a)' equal to zero and attempt to solve: Simplifying -1b + 4a = 0 Reorder the terms: 4a + -1b = 0 Solving 4a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 4a + -1b + b = 0 + b Combine like terms: -1b + b = 0 4a + 0 = 0 + b 4a = 0 + b Remove the zero: 4a = b Divide each side by '4'. a = 0.25b Simplifying a = 0.25b

Solution

a = {0, 0.25b}

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