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

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


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

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

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

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

Combine like terms: -8x + 72x = 64x
(-36 + 64x + 16x2) = 0

Solving
-36 + 64x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + 16x + 4x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-4.5, 0.5}

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