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

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


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

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

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

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

Combine like terms: 18x + -12x = 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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