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

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


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

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

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

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

Combine like terms: 9x + -8x = 1x
(-12 + 1x + 6x2) + -4x2 + 9 = 0

Reorder the terms:
-12 + 9 + 1x + 6x2 + -4x2 = 0

Combine like terms: -12 + 9 = -3
-3 + 1x + 6x2 + -4x2 = 0

Combine like terms: 6x2 + -4x2 = 2x2
-3 + 1x + 2x2 = 0

Solving
-3 + 1x + 2x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1.5, 1}

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