(5a+6b^2)(a-b^2)=0

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Solution for (5a+6b^2)(a-b^2)=0 equation: 


Simplifying
(5a + 6b2)(a + -1b2) = 0

Multiply (5a + 6b2) * (a + -1b2)
(5a * (a + -1b2) + 6b2 * (a + -1b2)) = 0
((a * 5a + -1b2 * 5a) + 6b2 * (a + -1b2)) = 0

Reorder the terms:
((-5ab2 + 5a2) + 6b2 * (a + -1b2)) = 0
((-5ab2 + 5a2) + 6b2 * (a + -1b2)) = 0
(-5ab2 + 5a2 + (a * 6b2 + -1b2 * 6b2)) = 0
(-5ab2 + 5a2 + (6ab2 + -6b4)) = 0

Reorder the terms:
(-5ab2 + 6ab2 + 5a2 + -6b4) = 0

Combine like terms: -5ab2 + 6ab2 = 1ab2
(1ab2 + 5a2 + -6b4) = 0

Solving
1ab2 + 5a2 + -6b4 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -1b2)(5a + 6b2) = 0


Subproblem 1
Set the factor '(a + -1b2)' equal to zero and attempt to solve:

Simplifying
a + -1b2 = 0

Solving
a + -1b2 = 0

Move all terms containing a to the left, all other terms to the right.

Add 'b2' to each side of the equation.
a + -1b2 + b2 = 0 + b2

Combine like terms: -1b2 + b2 = 0
a + 0 = 0 + b2
a = 0 + b2
Remove the zero:
a = b2

Simplifying
a = b2

Subproblem 2
Set the factor '(5a + 6b2)' equal to zero and attempt to solve:

Simplifying
5a + 6b2 = 0

Solving
5a + 6b2 = 0

Move all terms containing a to the left, all other terms to the right.

Add '-6b2' to each side of the equation.
5a + 6b2 + -6b2 = 0 + -6b2

Combine like terms: 6b2 + -6b2 = 0
5a + 0 = 0 + -6b2
5a = 0 + -6b2
Remove the zero:
5a = -6b2

Divide each side by '5'.
a = -1.2b2

Simplifying
a = -1.2b2
Solution
a = {b2, -1.2b2}

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