(4a+8x)(7a-5x)=

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Solution for (4a+8x)(7a-5x)= equation: 


Simplifying
(4a + 8x)(7a + -5x) = 0

Multiply (4a + 8x) * (7a + -5x)
(4a * (7a + -5x) + 8x * (7a + -5x)) = 0
((7a * 4a + -5x * 4a) + 8x * (7a + -5x)) = 0

Reorder the terms:
((-20ax + 28a2) + 8x * (7a + -5x)) = 0
((-20ax + 28a2) + 8x * (7a + -5x)) = 0
(-20ax + 28a2 + (7a * 8x + -5x * 8x)) = 0
(-20ax + 28a2 + (56ax + -40x2)) = 0

Reorder the terms:
(-20ax + 56ax + 28a2 + -40x2) = 0

Combine like terms: -20ax + 56ax = 36ax
(36ax + 28a2 + -40x2) = 0

Solving
36ax + 28a2 + -40x2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9ax + 7a2 + -10x2) = 0

Factor a trinomial.
4((7a + -5x)(a + 2x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7a + -5x)' equal to zero and attempt to solve:

Simplifying
7a + -5x = 0

Solving
7a + -5x = 0

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

Add '5x' to each side of the equation.
7a + -5x + 5x = 0 + 5x

Combine like terms: -5x + 5x = 0
7a + 0 = 0 + 5x
7a = 0 + 5x
Remove the zero:
7a = 5x

Divide each side by '7'.
a = 0.7142857143x

Simplifying
a = 0.7142857143x

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

Simplifying
a + 2x = 0

Solving
a + 2x = 0

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

Add '-2x' to each side of the equation.
a + 2x + -2x = 0 + -2x

Combine like terms: 2x + -2x = 0
a + 0 = 0 + -2x
a = 0 + -2x
Remove the zero:
a = -2x

Simplifying
a = -2x
Solution
a = {0.7142857143x, -2x}

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