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

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


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

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

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

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

Combine like terms: -2x + -9x = -11x
9x2 + -4 + (6 + -11x + 3x2) = 0

Reorder the terms:
-4 + 6 + -11x + 9x2 + 3x2 = 0

Combine like terms: -4 + 6 = 2
2 + -11x + 9x2 + 3x2 = 0

Combine like terms: 9x2 + 3x2 = 12x2
2 + -11x + 12x2 = 0

Solving
2 + -11x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -4x)(2 + -3x) = 0


Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0.25, 0.6666666667}

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