(3a+5)(2a-7)=

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Solution for (3a+5)(2a-7)= equation: 


Simplifying
(3a + 5)(2a + -7) = 0

Reorder the terms:
(5 + 3a)(2a + -7) = 0

Reorder the terms:
(5 + 3a)(-7 + 2a) = 0

Multiply (5 + 3a) * (-7 + 2a)
(5(-7 + 2a) + 3a * (-7 + 2a)) = 0
((-7 * 5 + 2a * 5) + 3a * (-7 + 2a)) = 0
((-35 + 10a) + 3a * (-7 + 2a)) = 0
(-35 + 10a + (-7 * 3a + 2a * 3a)) = 0
(-35 + 10a + (-21a + 6a2)) = 0

Combine like terms: 10a + -21a = -11a
(-35 + -11a + 6a2) = 0

Solving
-35 + -11a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -3a)(7 + -2a) = 0


Subproblem 1
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

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

Simplifying
7 + -2a = 0

Solving
7 + -2a = 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 + -2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2a = 0 + -7
-2a = 0 + -7

Combine like terms: 0 + -7 = -7
-2a = -7

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {-1.666666667, 3.5}

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