(7x-9)(4x+8)=0

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Solution for (7x-9)(4x+8)=0 equation: 


Simplifying
(7x + -9)(4x + 8) = 0

Reorder the terms:
(-9 + 7x)(4x + 8) = 0

Reorder the terms:
(-9 + 7x)(8 + 4x) = 0

Multiply (-9 + 7x) * (8 + 4x)
(-9(8 + 4x) + 7x * (8 + 4x)) = 0
((8 * -9 + 4x * -9) + 7x * (8 + 4x)) = 0
((-72 + -36x) + 7x * (8 + 4x)) = 0
(-72 + -36x + (8 * 7x + 4x * 7x)) = 0
(-72 + -36x + (56x + 28x2)) = 0

Combine like terms: -36x + 56x = 20x
(-72 + 20x + 28x2) = 0

Solving
-72 + 20x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 5x + 7x2) = 0

Factor a trinomial.
4((-2 + -1x)(9 + -7x)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(9 + -7x)' equal to zero and attempt to solve:

Simplifying
9 + -7x = 0

Solving
9 + -7x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x = 0 + -9
-7x = 0 + -9

Combine like terms: 0 + -9 = -9
-7x = -9

Divide each side by '-7'.
x = 1.285714286

Simplifying
x = 1.285714286
Solution
x = {-2, 1.285714286}

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