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

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


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

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

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

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

Combine like terms: 36x + 4x = 40x
(18 + 40x + 8x2) = 0

Solving
18 + 40x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 20x + 4x2) = 0

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

Ignore the factor 2.

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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