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

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


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

Reorder the terms:
(-5 + 3a)(4a + 7) = 0

Reorder the terms:
(-5 + 3a)(7 + 4a) = 0

Multiply (-5 + 3a) * (7 + 4a)
(-5(7 + 4a) + 3a * (7 + 4a)) = 0
((7 * -5 + 4a * -5) + 3a * (7 + 4a)) = 0
((-35 + -20a) + 3a * (7 + 4a)) = 0
(-35 + -20a + (7 * 3a + 4a * 3a)) = 0
(-35 + -20a + (21a + 12a2)) = 0

Combine like terms: -20a + 21a = 1a
(-35 + 1a + 12a2) = 0

Solving
-35 + 1a + 12a2 = 0

Solving for variable 'a'.

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


Subproblem 1
Set the factor '(-7 + -4a)' equal to zero and attempt to solve:

Simplifying
-7 + -4a = 0

Solving
-7 + -4a = 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 + -4a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4a = 0 + 7
-4a = 0 + 7

Combine like terms: 0 + 7 = 7
-4a = 7

Divide each side by '-4'.
a = -1.75

Simplifying
a = -1.75

Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3a = 0 + -5
-3a = 0 + -5

Combine like terms: 0 + -5 = -5
-3a = -5

Divide each side by '-3'.
a = 1.666666667

Simplifying
a = 1.666666667
Solution
a = {-1.75, 1.666666667}

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