6a(2a-5)-7(2a-5)=

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Solution for 6a(2a-5)-7(2a-5)= equation: 


Simplifying
6a(2a + -5) + -7(2a + -5) = 0

Reorder the terms:
6a(-5 + 2a) + -7(2a + -5) = 0
(-5 * 6a + 2a * 6a) + -7(2a + -5) = 0
(-30a + 12a2) + -7(2a + -5) = 0

Reorder the terms:
-30a + 12a2 + -7(-5 + 2a) = 0
-30a + 12a2 + (-5 * -7 + 2a * -7) = 0
-30a + 12a2 + (35 + -14a) = 0

Reorder the terms:
35 + -30a + -14a + 12a2 = 0

Combine like terms: -30a + -14a = -44a
35 + -44a + 12a2 = 0

Solving
35 + -44a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7 + -6a)(5 + -2a) = 0


Subproblem 1
Set the factor '(7 + -6a)' equal to zero and attempt to solve:

Simplifying
7 + -6a = 0

Solving
7 + -6a = 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 + -6a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6a = 0 + -7
-6a = 0 + -7

Combine like terms: 0 + -7 = -7
-6a = -7

Divide each side by '-6'.
a = 1.166666667

Simplifying
a = 1.166666667

Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 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 + -2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2a = 0 + -5
-2a = 0 + -5

Combine like terms: 0 + -5 = -5
-2a = -5

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
Solution
a = {1.166666667, 2.5}

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