(2x+3)(9-4x)=0

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Solution for (2x+3)(9-4x)=0 equation: 


Simplifying
(2x + 3)(9 + -4x) = 0

Reorder the terms:
(3 + 2x)(9 + -4x) = 0

Multiply (3 + 2x) * (9 + -4x)
(3(9 + -4x) + 2x * (9 + -4x)) = 0
((9 * 3 + -4x * 3) + 2x * (9 + -4x)) = 0
((27 + -12x) + 2x * (9 + -4x)) = 0
(27 + -12x + (9 * 2x + -4x * 2x)) = 0
(27 + -12x + (18x + -8x2)) = 0

Combine like terms: -12x + 18x = 6x
(27 + 6x + -8x2) = 0

Solving
27 + 6x + -8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -4x)(3 + 2x) = 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 '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {2.25, -1.5}

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