75=-5a(a+5)

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Solution for 75=-5a(a+5) equation: 


Simplifying
75 = -5a(a + 5)

Reorder the terms:
75 = -5a(5 + a)
75 = (5 * -5a + a * -5a)
75 = (-25a + -5a2)

Solving
75 = -25a + -5a2

Solving for variable 'a'.

Reorder the terms:
75 + 25a + 5a2 = -25a + 25a + -5a2 + 5a2

Combine like terms: -25a + 25a = 0
75 + 25a + 5a2 = 0 + -5a2 + 5a2
75 + 25a + 5a2 = -5a2 + 5a2

Combine like terms: -5a2 + 5a2 = 0
75 + 25a + 5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(15 + 5a + a2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(15 + 5a + a2)' equal to zero and attempt to solve:

Simplifying
15 + 5a + a2 = 0

Solving
15 + 5a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 5a + -15 + a2 = 0 + -15

Reorder the terms:
15 + -15 + 5a + a2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 5a + a2 = 0 + -15
5a + a2 = 0 + -15

Combine like terms: 0 + -15 = -15
5a + a2 = -15

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = -15 + 6.25

Reorder the terms:
6.25 + 5a + a2 = -15 + 6.25

Combine like terms: -15 + 6.25 = -8.75
6.25 + 5a + a2 = -8.75

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = -8.75

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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