(3a+7b)(4a-5b)=

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Solution for (3a+7b)(4a-5b)= equation:


Simplifying
(3a + 7b)(4a + -5b) = 0

Multiply (3a + 7b) * (4a + -5b)
(3a * (4a + -5b) + 7b * (4a + -5b)) = 0
((4a * 3a + -5b * 3a) + 7b * (4a + -5b)) = 0

Reorder the terms:
((-15ab + 12a2) + 7b * (4a + -5b)) = 0
((-15ab + 12a2) + 7b * (4a + -5b)) = 0
(-15ab + 12a2 + (4a * 7b + -5b * 7b)) = 0
(-15ab + 12a2 + (28ab + -35b2)) = 0

Reorder the terms:
(-15ab + 28ab + 12a2 + -35b2) = 0

Combine like terms: -15ab + 28ab = 13ab
(13ab + 12a2 + -35b2) = 0

Solving
13ab + 12a2 + -35b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -5b)(3a + 7b) = 0

Subproblem 1

Set the factor '(4a + -5b)' equal to zero and attempt to solve: Simplifying 4a + -5b = 0 Solving 4a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. 4a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 4a + 0 = 0 + 5b 4a = 0 + 5b Remove the zero: 4a = 5b Divide each side by '4'. a = 1.25b Simplifying a = 1.25b

Subproblem 2

Set the factor '(3a + 7b)' equal to zero and attempt to solve: Simplifying 3a + 7b = 0 Solving 3a + 7b = 0 Move all terms containing a to the left, all other terms to the right. Add '-7b' to each side of the equation. 3a + 7b + -7b = 0 + -7b Combine like terms: 7b + -7b = 0 3a + 0 = 0 + -7b 3a = 0 + -7b Remove the zero: 3a = -7b Divide each side by '3'. a = -2.333333333b Simplifying a = -2.333333333b

Solution

a = {1.25b, -2.333333333b}

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