(3a-7)(4a+8)=

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Solution for (3a-7)(4a+8)= equation: 


Simplifying
(3a + -7)(4a + 8) = 0

Reorder the terms:
(-7 + 3a)(4a + 8) = 0

Reorder the terms:
(-7 + 3a)(8 + 4a) = 0

Multiply (-7 + 3a) * (8 + 4a)
(-7(8 + 4a) + 3a * (8 + 4a)) = 0
((8 * -7 + 4a * -7) + 3a * (8 + 4a)) = 0
((-56 + -28a) + 3a * (8 + 4a)) = 0
(-56 + -28a + (8 * 3a + 4a * 3a)) = 0
(-56 + -28a + (24a + 12a2)) = 0

Combine like terms: -28a + 24a = -4a
(-56 + -4a + 12a2) = 0

Solving
-56 + -4a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + -1a + 3a2) = 0

Factor a trinomial.
4((-2 + -1a)(7 + -3a)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 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 + -1a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1a = 0 + 2
-1a = 0 + 2

Combine like terms: 0 + 2 = 2
-1a = 2

Divide each side by '-1'.
a = -2

Simplifying
a = -2

Subproblem 2
Set the factor '(7 + -3a)' equal to zero and attempt to solve:

Simplifying
7 + -3a = 0

Solving
7 + -3a = 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 + -3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3a = 0 + -7
-3a = 0 + -7

Combine like terms: 0 + -7 = -7
-3a = -7

Divide each side by '-3'.
a = 2.333333333

Simplifying
a = 2.333333333
Solution
a = {-2, 2.333333333}

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