5a^2+50ab+105b^2=0

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Solution for 5a^2+50ab+105b^2=0 equation:


Simplifying
5a2 + 50ab + 105b2 = 0

Reorder the terms:
50ab + 5a2 + 105b2 = 0

Solving
50ab + 5a2 + 105b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(10ab + a2 + 21b2) = 0

Factor a trinomial.
5((a + 3b)(a + 7b)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(a + 3b)' equal to zero and attempt to solve: Simplifying a + 3b = 0 Solving a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 a + 0 = 0 + -3b a = 0 + -3b Remove the zero: a = -3b Simplifying a = -3b

Subproblem 2

Set the factor '(a + 7b)' equal to zero and attempt to solve: Simplifying a + 7b = 0 Solving a + 7b = 0 Move all terms containing a to the left, all other terms to the right. Add '-7b' to each side of the equation. a + 7b + -7b = 0 + -7b Combine like terms: 7b + -7b = 0 a + 0 = 0 + -7b a = 0 + -7b Remove the zero: a = -7b Simplifying a = -7b

Solution

a = {-3b, -7b}

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