7+2a(a-3)=-9

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Solution for 7+2a(a-3)=-9 equation: 


Simplifying
7 + 2a(a + -3) = -9

Reorder the terms:
7 + 2a(-3 + a) = -9
7 + (-3 * 2a + a * 2a) = -9
7 + (-6a + 2a2) = -9

Solving
7 + -6a + 2a2 = -9

Solving for variable 'a'.

Reorder the terms:
7 + 9 + -6a + 2a2 = -9 + 9

Combine like terms: 7 + 9 = 16
16 + -6a + 2a2 = -9 + 9

Combine like terms: -9 + 9 = 0
16 + -6a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -3a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -3a + a2)' equal to zero and attempt to solve:

Simplifying
8 + -3a + a2 = 0

Solving
8 + -3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -3a + -8 + a2 = 0 + -8

Reorder the terms:
8 + -8 + -3a + a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3a + a2 = 0 + -8
-3a + a2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3a + a2 = -8

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 = -8 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -8 + 2.25

Combine like terms: -8 + 2.25 = -5.75
2.25 + -3a + a2 = -5.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = -5.75

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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