(7a+4b)(-4b-7a)=

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Solution for (7a+4b)(-4b-7a)= equation: 


Simplifying
(7a + 4b)(-4b + -7a) = 0

Reorder the terms:
(7a + 4b)(-7a + -4b) = 0

Multiply (7a + 4b) * (-7a + -4b)
(7a * (-7a + -4b) + 4b * (-7a + -4b)) = 0
((-7a * 7a + -4b * 7a) + 4b * (-7a + -4b)) = 0

Reorder the terms:
((-28ab + -49a2) + 4b * (-7a + -4b)) = 0
((-28ab + -49a2) + 4b * (-7a + -4b)) = 0
(-28ab + -49a2 + (-7a * 4b + -4b * 4b)) = 0
(-28ab + -49a2 + (-28ab + -16b2)) = 0

Reorder the terms:
(-28ab + -28ab + -49a2 + -16b2) = 0

Combine like terms: -28ab + -28ab = -56ab
(-56ab + -49a2 + -16b2) = 0

Solving
-56ab + -49a2 + -16b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(56ab + 49a2 + 16b2) = 0

Factor a trinomial.
-1((7a + 4b)(7a + 4b)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7a + 4b)' equal to zero and attempt to solve:

Simplifying
7a + 4b = 0

Solving
7a + 4b = 0

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

Add '-4b' to each side of the equation.
7a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
7a + 0 = 0 + -4b
7a = 0 + -4b
Remove the zero:
7a = -4b

Divide each side by '7'.
a = -0.5714285714b

Simplifying
a = -0.5714285714b

Subproblem 2
Set the factor '(7a + 4b)' equal to zero and attempt to solve:

Simplifying
7a + 4b = 0

Solving
7a + 4b = 0

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

Add '-4b' to each side of the equation.
7a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
7a + 0 = 0 + -4b
7a = 0 + -4b
Remove the zero:
7a = -4b

Divide each side by '7'.
a = -0.5714285714b

Simplifying
a = -0.5714285714b
Solution
a = {-0.5714285714b, -0.5714285714b}

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