15a^2-4a=3-7a

Solution for 15a^2-4a=3-7a equation:

Simplifying
15a2 + -4a = 3 + -7a

Reorder the terms:
-4a + 15a2 = 3 + -7a

Solving
-4a + 15a2 = 3 + -7a

Solving for variable 'a'.

Reorder the terms:
-3 + -4a + 7a + 15a2 = 3 + -7a + -3 + 7a

Combine like terms: -4a + 7a = 3a
-3 + 3a + 15a2 = 3 + -7a + -3 + 7a

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

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + a + 5a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + a + 5a2)' equal to zero and attempt to solve:

Simplifying
-1 + a + 5a2 = 0

Solving
-1 + a + 5a2 = 0

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

Divide each side by '5'.
-0.2 + 0.2a + a2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.2a + 0.2 + a2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.2a + a2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.2a + a2 = 0 + 0.2
0.2a + a2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
0.2a + a2 = 0.2

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2a + 0.25 + a2 = 0.2 + 0.25

Reorder the terms:
0.25 + 0.2a + a2 = 0.2 + 0.25

Combine like terms: 0.2 + 0.25 = 0.45
0.25 + 0.2a + a2 = 0.45

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(a + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1
a + 0.5 = 0.670820393

Simplifying
a + 0.5 = 0.670820393

Reorder the terms:
0.5 + a = 0.670820393

Solving
0.5 + a = 0.670820393

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 0.670820393 + -0.5
a = 0.670820393 + -0.5

Combine like terms: 0.670820393 + -0.5 = 0.170820393
a = 0.170820393

Simplifying
a = 0.170820393

Subproblem 2
a + 0.5 = -0.670820393

Simplifying
a + 0.5 = -0.670820393

Reorder the terms:
0.5 + a = -0.670820393

Solving
0.5 + a = -0.670820393

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -0.670820393 + -0.5
a = -0.670820393 + -0.5

Combine like terms: -0.670820393 + -0.5 = -1.170820393
a = -1.170820393

Simplifying
a = -1.170820393

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.170820393, -1.170820393}
Solution
a = {0.170820393, -1.170820393}