(4x^2-6x+9)(2x+3)=0

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Solution for (4x^2-6x+9)(2x+3)=0 equation:


Simplifying
(4x2 + -6x + 9)(2x + 3) = 0

Reorder the terms:
(9 + -6x + 4x2)(2x + 3) = 0

Reorder the terms:
(9 + -6x + 4x2)(3 + 2x) = 0

Multiply (9 + -6x + 4x2) * (3 + 2x)
(9(3 + 2x) + -6x * (3 + 2x) + 4x2 * (3 + 2x)) = 0
((3 * 9 + 2x * 9) + -6x * (3 + 2x) + 4x2 * (3 + 2x)) = 0
((27 + 18x) + -6x * (3 + 2x) + 4x2 * (3 + 2x)) = 0
(27 + 18x + (3 * -6x + 2x * -6x) + 4x2 * (3 + 2x)) = 0
(27 + 18x + (-18x + -12x2) + 4x2 * (3 + 2x)) = 0
(27 + 18x + -18x + -12x2 + (3 * 4x2 + 2x * 4x2)) = 0
(27 + 18x + -18x + -12x2 + (12x2 + 8x3)) = 0

Combine like terms: 18x + -18x = 0
(27 + 0 + -12x2 + 12x2 + 8x3) = 0
(27 + -12x2 + 12x2 + 8x3) = 0

Combine like terms: -12x2 + 12x2 = 0
(27 + 0 + 8x3) = 0
(27 + 8x3) = 0

Solving
27 + 8x3 = 0

Solving for variable 'x'.

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

Add '-27' to each side of the equation.
27 + -27 + 8x3 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 8x3 = 0 + -27
8x3 = 0 + -27

Combine like terms: 0 + -27 = -27
8x3 = -27

Divide each side by '8'.
x3 = -3.375

Simplifying
x3 = -3.375

Reorder the terms:
3.375 + x3 = -3.375 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
3.375 + x3 = 0.000

The solution to this equation could not be determined.

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