3a(8a-10)=5(7a+5)

Solution for 3a(8a-10)=5(7a+5) equation:

Simplifying
3a(8a + -10) = 5(7a + 5)

Reorder the terms:
3a(-10 + 8a) = 5(7a + 5)
(-10 * 3a + 8a * 3a) = 5(7a + 5)
(-30a + 24a2) = 5(7a + 5)

Reorder the terms:
-30a + 24a2 = 5(5 + 7a)
-30a + 24a2 = (5 * 5 + 7a * 5)
-30a + 24a2 = (25 + 35a)

Solving
-30a + 24a2 = 25 + 35a

Solving for variable 'a'.

Reorder the terms:
-25 + -30a + -35a + 24a2 = 25 + 35a + -25 + -35a

Combine like terms: -30a + -35a = -65a
-25 + -65a + 24a2 = 25 + 35a + -25 + -35a

Reorder the terms:
-25 + -65a + 24a2 = 25 + -25 + 35a + -35a

Combine like terms: 25 + -25 = 0
-25 + -65a + 24a2 = 0 + 35a + -35a
-25 + -65a + 24a2 = 35a + -35a

Combine like terms: 35a + -35a = 0
-25 + -65a + 24a2 = 0

Begin completing the square.  Divide all terms by
24 the coefficient of the squared term: 

Divide each side by '24'.
-1.041666667 + -2.708333333a + a2 = 0

Move the constant term to the right:

Add '1.041666667' to each side of the equation.
-1.041666667 + -2.708333333a + 1.041666667 + a2 = 0 + 1.041666667

Reorder the terms:
-1.041666667 + 1.041666667 + -2.708333333a + a2 = 0 + 1.041666667

Combine like terms: -1.041666667 + 1.041666667 = 0.000000000
0.000000000 + -2.708333333a + a2 = 0 + 1.041666667
-2.708333333a + a2 = 0 + 1.041666667

Combine like terms: 0 + 1.041666667 = 1.041666667
-2.708333333a + a2 = 1.041666667

The a term is -2.708333333a.  Take half its coefficient (-1.354166667).
Square it (1.833767362) and add it to both sides.

Add '1.833767362' to each side of the equation.
-2.708333333a + 1.833767362 + a2 = 1.041666667 + 1.833767362

Reorder the terms:
1.833767362 + -2.708333333a + a2 = 1.041666667 + 1.833767362

Combine like terms: 1.041666667 + 1.833767362 = 2.875434029
1.833767362 + -2.708333333a + a2 = 2.875434029

Factor a perfect square on the left side:
(a + -1.354166667)(a + -1.354166667) = 2.875434029

Calculate the square root of the right side: 1.695710479

Break this problem into two subproblems by setting 
(a + -1.354166667) equal to 1.695710479 and -1.695710479.

Subproblem 1
a + -1.354166667 = 1.695710479

Simplifying
a + -1.354166667 = 1.695710479

Reorder the terms:
-1.354166667 + a = 1.695710479

Solving
-1.354166667 + a = 1.695710479

Solving for variable 'a'.

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

Add '1.354166667' to each side of the equation.
-1.354166667 + 1.354166667 + a = 1.695710479 + 1.354166667

Combine like terms: -1.354166667 + 1.354166667 = 0.000000000
0.000000000 + a = 1.695710479 + 1.354166667
a = 1.695710479 + 1.354166667

Combine like terms: 1.695710479 + 1.354166667 = 3.049877146
a = 3.049877146

Simplifying
a = 3.049877146

Subproblem 2
a + -1.354166667 = -1.695710479

Simplifying
a + -1.354166667 = -1.695710479

Reorder the terms:
-1.354166667 + a = -1.695710479

Solving
-1.354166667 + a = -1.695710479

Solving for variable 'a'.

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

Add '1.354166667' to each side of the equation.
-1.354166667 + 1.354166667 + a = -1.695710479 + 1.354166667

Combine like terms: -1.354166667 + 1.354166667 = 0.000000000
0.000000000 + a = -1.695710479 + 1.354166667
a = -1.695710479 + 1.354166667

Combine like terms: -1.695710479 + 1.354166667 = -0.341543812
a = -0.341543812

Simplifying
a = -0.341543812

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.049877146, -0.341543812}