4-6a*4a=1-5(7-2a)

Solution for 4-6a*4a=1-5(7-2a) equation:

Simplifying
4 + -6a * 4a = 1 + -5(7 + -2a)

Reorder the terms for easier multiplication:
4 + -6 * 4a * a = 1 + -5(7 + -2a)

Multiply -6 * 4
4 + -24a * a = 1 + -5(7 + -2a)

Multiply a * a
4 + -24a2 = 1 + -5(7 + -2a)
4 + -24a2 = 1 + (7 * -5 + -2a * -5)
4 + -24a2 = 1 + (-35 + 10a)

Combine like terms: 1 + -35 = -34
4 + -24a2 = -34 + 10a

Solving
4 + -24a2 = -34 + 10a

Solving for variable 'a'.

Reorder the terms:
4 + 34 + -10a + -24a2 = -34 + 10a + 34 + -10a

Combine like terms: 4 + 34 = 38
38 + -10a + -24a2 = -34 + 10a + 34 + -10a

Reorder the terms:
38 + -10a + -24a2 = -34 + 34 + 10a + -10a

Combine like terms: -34 + 34 = 0
38 + -10a + -24a2 = 0 + 10a + -10a
38 + -10a + -24a2 = 10a + -10a

Combine like terms: 10a + -10a = 0
38 + -10a + -24a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(19 + -5a + -12a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(19 + -5a + -12a2)' equal to zero and attempt to solve:

Simplifying
19 + -5a + -12a2 = 0

Solving
19 + -5a + -12a2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-1.583333333 + 0.4166666667a + a2 = 0

Move the constant term to the right:

Add '1.583333333' to each side of the equation.
-1.583333333 + 0.4166666667a + 1.583333333 + a2 = 0 + 1.583333333

Reorder the terms:
-1.583333333 + 1.583333333 + 0.4166666667a + a2 = 0 + 1.583333333

Combine like terms: -1.583333333 + 1.583333333 = 0.000000000
0.000000000 + 0.4166666667a + a2 = 0 + 1.583333333
0.4166666667a + a2 = 0 + 1.583333333

Combine like terms: 0 + 1.583333333 = 1.583333333
0.4166666667a + a2 = 1.583333333

The a term is 0.4166666667a.  Take half its coefficient (0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
0.4166666667a + 0.04340277781 + a2 = 1.583333333 + 0.04340277781

Reorder the terms:
0.04340277781 + 0.4166666667a + a2 = 1.583333333 + 0.04340277781

Combine like terms: 1.583333333 + 0.04340277781 = 1.62673611081
0.04340277781 + 0.4166666667a + a2 = 1.62673611081

Factor a perfect square on the left side:
(a + 0.2083333334)(a + 0.2083333334) = 1.62673611081

Calculate the square root of the right side: 1.275435655

Break this problem into two subproblems by setting 
(a + 0.2083333334) equal to 1.275435655 and -1.275435655.

Subproblem 1
a + 0.2083333334 = 1.275435655

Simplifying
a + 0.2083333334 = 1.275435655

Reorder the terms:
0.2083333334 + a = 1.275435655

Solving
0.2083333334 + a = 1.275435655

Solving for variable 'a'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + a = 1.275435655 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + a = 1.275435655 + -0.2083333334
a = 1.275435655 + -0.2083333334

Combine like terms: 1.275435655 + -0.2083333334 = 1.0671023216
a = 1.0671023216

Simplifying
a = 1.0671023216

Subproblem 2
a + 0.2083333334 = -1.275435655

Simplifying
a + 0.2083333334 = -1.275435655

Reorder the terms:
0.2083333334 + a = -1.275435655

Solving
0.2083333334 + a = -1.275435655

Solving for variable 'a'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + a = -1.275435655 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + a = -1.275435655 + -0.2083333334
a = -1.275435655 + -0.2083333334

Combine like terms: -1.275435655 + -0.2083333334 = -1.4837689884
a = -1.4837689884

Simplifying
a = -1.4837689884

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.0671023216, -1.4837689884}
Solution
a = {1.0671023216, -1.4837689884}