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

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


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

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

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

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

Combine like terms: -36x + 4x = -32x
(-8 + -32x + 18x2) = 0

Solving
-8 + -32x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -16x + 9x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -9x)' equal to zero and attempt to solve:

Simplifying
-2 + -9x = 0

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

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

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

Divide each side by '-9'.
x = -0.2222222222

Simplifying
x = -0.2222222222

Subproblem 2
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
Solution
x = {-0.2222222222, 2}

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