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

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


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

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

Remove parenthesis around (-9 + 4x2)
-9 + 4x2 + -2(2x + -3) + x(2x + -3) = 0

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

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

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

Combine like terms: -9 + 6 = -3
-3 + -4x + -3x + 4x2 + 2x2 = 0

Combine like terms: -4x + -3x = -7x
-3 + -7x + 4x2 + 2x2 = 0

Combine like terms: 4x2 + 2x2 = 6x2
-3 + -7x + 6x2 = 0

Solving
-3 + -7x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -3x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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 = {-0.3333333333, 1.5}

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