15a^2-3=3-7a

Solution for 15a^2-3=3-7a equation:

Simplifying
15a2 + -3 = 3 + -7a

Reorder the terms:
-3 + 15a2 = 3 + -7a

Solving
-3 + 15a2 = 3 + -7a

Solving for variable 'a'.

Reorder the terms:
-3 + -3 + 7a + 15a2 = 3 + -7a + -3 + 7a

Combine like terms: -3 + -3 = -6
-6 + 7a + 15a2 = 3 + -7a + -3 + 7a

Reorder the terms:
-6 + 7a + 15a2 = 3 + -3 + -7a + 7a

Combine like terms: 3 + -3 = 0
-6 + 7a + 15a2 = 0 + -7a + 7a
-6 + 7a + 15a2 = -7a + 7a

Combine like terms: -7a + 7a = 0
-6 + 7a + 15a2 = 0

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

Divide each side by '15'.
-0.4 + 0.4666666667a + a2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.4666666667a + 0.4 + a2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.4666666667a + a2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.4666666667a + a2 = 0 + 0.4
0.4666666667a + a2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.4666666667a + a2 = 0.4

The a term is 0.4666666667a.  Take half its coefficient (0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
0.4666666667a + 0.05444444448 + a2 = 0.4 + 0.05444444448

Reorder the terms:
0.05444444448 + 0.4666666667a + a2 = 0.4 + 0.05444444448

Combine like terms: 0.4 + 0.05444444448 = 0.45444444448
0.05444444448 + 0.4666666667a + a2 = 0.45444444448

Factor a perfect square on the left side:
(a + 0.2333333334)(a + 0.2333333334) = 0.45444444448

Calculate the square root of the right side: 0.674124947

Break this problem into two subproblems by setting 
(a + 0.2333333334) equal to 0.674124947 and -0.674124947.

Subproblem 1
a + 0.2333333334 = 0.674124947

Simplifying
a + 0.2333333334 = 0.674124947

Reorder the terms:
0.2333333334 + a = 0.674124947

Solving
0.2333333334 + a = 0.674124947

Solving for variable 'a'.

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

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + a = 0.674124947 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + a = 0.674124947 + -0.2333333334
a = 0.674124947 + -0.2333333334

Combine like terms: 0.674124947 + -0.2333333334 = 0.4407916136
a = 0.4407916136

Simplifying
a = 0.4407916136

Subproblem 2
a + 0.2333333334 = -0.674124947

Simplifying
a + 0.2333333334 = -0.674124947

Reorder the terms:
0.2333333334 + a = -0.674124947

Solving
0.2333333334 + a = -0.674124947

Solving for variable 'a'.

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

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + a = -0.674124947 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + a = -0.674124947 + -0.2333333334
a = -0.674124947 + -0.2333333334

Combine like terms: -0.674124947 + -0.2333333334 = -0.9074582804
a = -0.9074582804

Simplifying
a = -0.9074582804

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.4407916136, -0.9074582804}