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

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


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

Reorder the terms:
-4x(2 + x) + 9(x + 2) = 0
(2 * -4x + x * -4x) + 9(x + 2) = 0
(-8x + -4x2) + 9(x + 2) = 0

Reorder the terms:
-8x + -4x2 + 9(2 + x) = 0
-8x + -4x2 + (2 * 9 + x * 9) = 0
-8x + -4x2 + (18 + 9x) = 0

Reorder the terms:
18 + -8x + 9x + -4x2 = 0

Combine like terms: -8x + 9x = 1x
18 + 1x + -4x2 = 0

Solving
18 + 1x + -4x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {2.25, -2}

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