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

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


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

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

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

Multiply (4 + -5a) * (-7 + 3a)
(4(-7 + 3a) + -5a * (-7 + 3a)) = 0
((-7 * 4 + 3a * 4) + -5a * (-7 + 3a)) = 0
((-28 + 12a) + -5a * (-7 + 3a)) = 0
(-28 + 12a + (-7 * -5a + 3a * -5a)) = 0
(-28 + 12a + (35a + -15a2)) = 0

Combine like terms: 12a + 35a = 47a
(-28 + 47a + -15a2) = 0

Solving
-28 + 47a + -15a2 = 0

Solving for variable 'a'.

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


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 '(4 + -5a)' equal to zero and attempt to solve:

Simplifying
4 + -5a = 0

Solving
4 + -5a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5a = 0 + -4
-5a = 0 + -4

Combine like terms: 0 + -4 = -4
-5a = -4

Divide each side by '-5'.
a = 0.8

Simplifying
a = 0.8
Solution
a = {2.333333333, 0.8}

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