18-69=4a(a+3)

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Solution for 18-69=4a(a+3) equation: 


Simplifying
18 + -69 = 4a(a + 3)

Combine like terms: 18 + -69 = -51
-51 = 4a(a + 3)

Reorder the terms:
-51 = 4a(3 + a)
-51 = (3 * 4a + a * 4a)
-51 = (12a + 4a2)

Solving
-51 = 12a + 4a2

Solving for variable 'a'.

Reorder the terms:
-51 + -12a + -4a2 = 12a + -12a + 4a2 + -4a2

Combine like terms: 12a + -12a = 0
-51 + -12a + -4a2 = 0 + 4a2 + -4a2
-51 + -12a + -4a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
-51 + -12a + -4a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(51 + 12a + 4a2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(51 + 12a + 4a2)' equal to zero and attempt to solve:

Simplifying
51 + 12a + 4a2 = 0

Solving
51 + 12a + 4a2 = 0

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

Divide each side by '4'.
12.75 + 3a + a2 = 0

Move the constant term to the right:

Add '-12.75' to each side of the equation.
12.75 + 3a + -12.75 + a2 = 0 + -12.75

Reorder the terms:
12.75 + -12.75 + 3a + a2 = 0 + -12.75

Combine like terms: 12.75 + -12.75 = 0.00
0.00 + 3a + a2 = 0 + -12.75
3a + a2 = 0 + -12.75

Combine like terms: 0 + -12.75 = -12.75
3a + a2 = -12.75

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = -12.75 + 2.25

Reorder the terms:
2.25 + 3a + a2 = -12.75 + 2.25

Combine like terms: -12.75 + 2.25 = -10.5
2.25 + 3a + a2 = -10.5

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = -10.5

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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