(4x+8)(2x-9)=0

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Solution for (4x+8)(2x-9)=0 equation: 


Simplifying
(4x + 8)(2x + -9) = 0

Reorder the terms:
(8 + 4x)(2x + -9) = 0

Reorder the terms:
(8 + 4x)(-9 + 2x) = 0

Multiply (8 + 4x) * (-9 + 2x)
(8(-9 + 2x) + 4x * (-9 + 2x)) = 0
((-9 * 8 + 2x * 8) + 4x * (-9 + 2x)) = 0
((-72 + 16x) + 4x * (-9 + 2x)) = 0
(-72 + 16x + (-9 * 4x + 2x * 4x)) = 0
(-72 + 16x + (-36x + 8x2)) = 0

Combine like terms: 16x + -36x = -20x
(-72 + -20x + 8x2) = 0

Solving
-72 + -20x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -5x + 2x2) = 0

Factor a trinomial.
4((-2 + -1x)(9 + -2x)) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-2, 4.5}

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