4x(x+2)=3x+9

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Solution for 4x(x+2)=3x+9 equation: 


Simplifying
4x(x + 2) = 3x + 9

Reorder the terms:
4x(2 + x) = 3x + 9
(2 * 4x + x * 4x) = 3x + 9
(8x + 4x2) = 3x + 9

Reorder the terms:
8x + 4x2 = 9 + 3x

Solving
8x + 4x2 = 9 + 3x

Solving for variable 'x'.

Reorder the terms:
-9 + 8x + -3x + 4x2 = 9 + 3x + -9 + -3x

Combine like terms: 8x + -3x = 5x
-9 + 5x + 4x2 = 9 + 3x + -9 + -3x

Reorder the terms:
-9 + 5x + 4x2 = 9 + -9 + 3x + -3x

Combine like terms: 9 + -9 = 0
-9 + 5x + 4x2 = 0 + 3x + -3x
-9 + 5x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-9 + 5x + 4x2 = 0

Factor a trinomial.
(-9 + -4x)(1 + -1x) = 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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-2.25, 1}

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