(3a+4b)(a-6b)=

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Solution for (3a+4b)(a-6b)= equation:


Simplifying
(3a + 4b)(a + -6b) = 0

Multiply (3a + 4b) * (a + -6b)
(3a * (a + -6b) + 4b * (a + -6b)) = 0
((a * 3a + -6b * 3a) + 4b * (a + -6b)) = 0

Reorder the terms:
((-18ab + 3a2) + 4b * (a + -6b)) = 0
((-18ab + 3a2) + 4b * (a + -6b)) = 0
(-18ab + 3a2 + (a * 4b + -6b * 4b)) = 0
(-18ab + 3a2 + (4ab + -24b2)) = 0

Reorder the terms:
(-18ab + 4ab + 3a2 + -24b2) = 0

Combine like terms: -18ab + 4ab = -14ab
(-14ab + 3a2 + -24b2) = 0

Solving
-14ab + 3a2 + -24b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -6b)(3a + 4b) = 0

Subproblem 1

Set the factor '(a + -6b)' equal to zero and attempt to solve: Simplifying a + -6b = 0 Solving a + -6b = 0 Move all terms containing a to the left, all other terms to the right. Add '6b' to each side of the equation. a + -6b + 6b = 0 + 6b Combine like terms: -6b + 6b = 0 a + 0 = 0 + 6b a = 0 + 6b Remove the zero: a = 6b Simplifying a = 6b

Subproblem 2

Set the factor '(3a + 4b)' equal to zero and attempt to solve: Simplifying 3a + 4b = 0 Solving 3a + 4b = 0 Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 3a + 4b + -4b = 0 + -4b Combine like terms: 4b + -4b = 0 3a + 0 = 0 + -4b 3a = 0 + -4b Remove the zero: 3a = -4b Divide each side by '3'. a = -1.333333333b Simplifying a = -1.333333333b

Solution

a = {6b, -1.333333333b}

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