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

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


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

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

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

Multiply (-2 + 3a) * (-5 + 2a)
(-2(-5 + 2a) + 3a * (-5 + 2a)) + (3a + -2)(-2a + 7) = 0
((-5 * -2 + 2a * -2) + 3a * (-5 + 2a)) + (3a + -2)(-2a + 7) = 0
((10 + -4a) + 3a * (-5 + 2a)) + (3a + -2)(-2a + 7) = 0
(10 + -4a + (-5 * 3a + 2a * 3a)) + (3a + -2)(-2a + 7) = 0
(10 + -4a + (-15a + 6a2)) + (3a + -2)(-2a + 7) = 0

Combine like terms: -4a + -15a = -19a
(10 + -19a + 6a2) + (3a + -2)(-2a + 7) = 0

Reorder the terms:
10 + -19a + 6a2 + (-2 + 3a)(-2a + 7) = 0

Reorder the terms:
10 + -19a + 6a2 + (-2 + 3a)(7 + -2a) = 0

Multiply (-2 + 3a) * (7 + -2a)
10 + -19a + 6a2 + (-2(7 + -2a) + 3a * (7 + -2a)) = 0
10 + -19a + 6a2 + ((7 * -2 + -2a * -2) + 3a * (7 + -2a)) = 0
10 + -19a + 6a2 + ((-14 + 4a) + 3a * (7 + -2a)) = 0
10 + -19a + 6a2 + (-14 + 4a + (7 * 3a + -2a * 3a)) = 0
10 + -19a + 6a2 + (-14 + 4a + (21a + -6a2)) = 0

Combine like terms: 4a + 21a = 25a
10 + -19a + 6a2 + (-14 + 25a + -6a2) = 0

Reorder the terms:
10 + -14 + -19a + 25a + 6a2 + -6a2 = 0

Combine like terms: 10 + -14 = -4
-4 + -19a + 25a + 6a2 + -6a2 = 0

Combine like terms: -19a + 25a = 6a
-4 + 6a + 6a2 + -6a2 = 0

Combine like terms: 6a2 + -6a2 = 0
-4 + 6a + 0 = 0
-4 + 6a = 0

Solving
-4 + 6a = 0

Solving for variable 'a'.

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

Add '4' to each side of the equation.
-4 + 4 + 6a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6a = 0 + 4
6a = 0 + 4

Combine like terms: 0 + 4 = 4
6a = 4

Divide each side by '6'.
a = 0.6666666667

Simplifying
a = 0.6666666667

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