(4x+9)(2x-1)=0

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Solution for (4x+9)(2x-1)=0 equation: 


Simplifying
(4x + 9)(2x + -1) = 0

Reorder the terms:
(9 + 4x)(2x + -1) = 0

Reorder the terms:
(9 + 4x)(-1 + 2x) = 0

Multiply (9 + 4x) * (-1 + 2x)
(9(-1 + 2x) + 4x * (-1 + 2x)) = 0
((-1 * 9 + 2x * 9) + 4x * (-1 + 2x)) = 0
((-9 + 18x) + 4x * (-1 + 2x)) = 0
(-9 + 18x + (-1 * 4x + 2x * 4x)) = 0
(-9 + 18x + (-4x + 8x2)) = 0

Combine like terms: 18x + -4x = 14x
(-9 + 14x + 8x2) = 0

Solving
-9 + 14x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -4x)(1 + -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 '(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 = {-2.25, 0.5}

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