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

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Solution for (-3a+7)(4a-8)=0 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 = 52a
(-56 + 52a + -12a2) = 0

Solving
-56 + 52a + -12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 13a + -3a2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
a = {2.333333333, 2}

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