3a(-5a-1)=17

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Solution for 3a(-5a-1)=17 equation: 


Simplifying
3a(-5a + -1) = 17

Reorder the terms:
3a(-1 + -5a) = 17
(-1 * 3a + -5a * 3a) = 17
(-3a + -15a2) = 17

Solving
-3a + -15a2 = 17

Solving for variable 'a'.

Reorder the terms:
-17 + -3a + -15a2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + -3a + -15a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(17 + 3a + 15a2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(17 + 3a + 15a2)' equal to zero and attempt to solve:

Simplifying
17 + 3a + 15a2 = 0

Solving
17 + 3a + 15a2 = 0

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

Divide each side by '15'.
1.133333333 + 0.2a + a2 = 0

Move the constant term to the right:

Add '-1.133333333' to each side of the equation.
1.133333333 + 0.2a + -1.133333333 + a2 = 0 + -1.133333333

Reorder the terms:
1.133333333 + -1.133333333 + 0.2a + a2 = 0 + -1.133333333

Combine like terms: 1.133333333 + -1.133333333 = 0.000000000
0.000000000 + 0.2a + a2 = 0 + -1.133333333
0.2a + a2 = 0 + -1.133333333

Combine like terms: 0 + -1.133333333 = -1.133333333
0.2a + a2 = -1.133333333

The a term is 0.2a.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2a + 0.01 + a2 = -1.133333333 + 0.01

Reorder the terms:
0.01 + 0.2a + a2 = -1.133333333 + 0.01

Combine like terms: -1.133333333 + 0.01 = -1.123333333
0.01 + 0.2a + a2 = -1.123333333

Factor a perfect square on the left side:
(a + 0.1)(a + 0.1) = -1.123333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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