(4ab+2)(3ab-7)=

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Solution for (4ab+2)(3ab-7)= equation: 


Simplifying
(4ab + 2)(3ab + -7) = 0

Reorder the terms:
(2 + 4ab)(3ab + -7) = 0

Reorder the terms:
(2 + 4ab)(-7 + 3ab) = 0

Multiply (2 + 4ab) * (-7 + 3ab)
(2(-7 + 3ab) + 4ab * (-7 + 3ab)) = 0
((-7 * 2 + 3ab * 2) + 4ab * (-7 + 3ab)) = 0
((-14 + 6ab) + 4ab * (-7 + 3ab)) = 0
(-14 + 6ab + (-7 * 4ab + 3ab * 4ab)) = 0
(-14 + 6ab + (-28ab + 12a2b2)) = 0

Combine like terms: 6ab + -28ab = -22ab
(-14 + -22ab + 12a2b2) = 0

Solving
-14 + -22ab + 12a2b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -11ab + 6a2b2) = 0

Factor a trinomial.
2((-1 + -2ab)(7 + -3ab)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -2ab)' equal to zero and attempt to solve:

Simplifying
-1 + -2ab = 0

Solving
-1 + -2ab = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2ab = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2ab = 0 + 1
-2ab = 0 + 1

Combine like terms: 0 + 1 = 1
-2ab = 1

Divide each side by '-2b'.
a = -0.5b-1

Simplifying
a = -0.5b-1

Subproblem 2
Set the factor '(7 + -3ab)' equal to zero and attempt to solve:

Simplifying
7 + -3ab = 0

Solving
7 + -3ab = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3ab = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3ab = 0 + -7
-3ab = 0 + -7

Combine like terms: 0 + -7 = -7
-3ab = -7

Divide each side by '-3b'.
a = 2.333333333b-1

Simplifying
a = 2.333333333b-1
Solution
a = {-0.5b-1, 2.333333333b-1}

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