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

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Solution for (4a-7)(3a+8)=0 equation: 


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

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

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

Multiply (-7 + 4a) * (8 + 3a)
(-7(8 + 3a) + 4a * (8 + 3a)) = 0
((8 * -7 + 3a * -7) + 4a * (8 + 3a)) = 0
((-56 + -21a) + 4a * (8 + 3a)) = 0
(-56 + -21a + (8 * 4a + 3a * 4a)) = 0
(-56 + -21a + (32a + 12a2)) = 0

Combine like terms: -21a + 32a = 11a
(-56 + 11a + 12a2) = 0

Solving
-56 + 11a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-8 + -3a)(7 + -4a) = 0


Subproblem 1
Set the factor '(-8 + -3a)' equal to zero and attempt to solve:

Simplifying
-8 + -3a = 0

Solving
-8 + -3a = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3a = 0 + 8
-3a = 0 + 8

Combine like terms: 0 + 8 = 8
-3a = 8

Divide each side by '-3'.
a = -2.666666667

Simplifying
a = -2.666666667

Subproblem 2
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
Solution
a = {-2.666666667, 1.75}

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