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

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


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

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

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

Multiply (-9 + 2x) * (4 + 2x)
(-9(4 + 2x) + 2x * (4 + 2x)) = 0
((4 * -9 + 2x * -9) + 2x * (4 + 2x)) = 0
((-36 + -18x) + 2x * (4 + 2x)) = 0
(-36 + -18x + (4 * 2x + 2x * 2x)) = 0
(-36 + -18x + (8x + 4x2)) = 0

Combine like terms: -18x + 8x = -10x
(-36 + -10x + 4x2) = 0

Solving
-36 + -10x + 4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

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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