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

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


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

Reorder the terms:
4x(9 + x) = 2(x + 9)
(9 * 4x + x * 4x) = 2(x + 9)
(36x + 4x2) = 2(x + 9)

Reorder the terms:
36x + 4x2 = 2(9 + x)
36x + 4x2 = (9 * 2 + x * 2)
36x + 4x2 = (18 + 2x)

Solving
36x + 4x2 = 18 + 2x

Solving for variable 'x'.

Reorder the terms:
-18 + 36x + -2x + 4x2 = 18 + 2x + -18 + -2x

Combine like terms: 36x + -2x = 34x
-18 + 34x + 4x2 = 18 + 2x + -18 + -2x

Reorder the terms:
-18 + 34x + 4x2 = 18 + -18 + 2x + -2x

Combine like terms: 18 + -18 = 0
-18 + 34x + 4x2 = 0 + 2x + -2x
-18 + 34x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-18 + 34x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 17x + 2x2) = 0

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

Ignore the factor 2.

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

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 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 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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 = {-9, 0.5}

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