(2x-3)(3x+2)-6(x-2)(x+3)=-3

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Solution for (2x-3)(3x+2)-6(x-2)(x+3)=-3 equation:


Simplifying
(2x + -3)(3x + 2) + -6(x + -2)(x + 3) = -3

Reorder the terms:
(-3 + 2x)(3x + 2) + -6(x + -2)(x + 3) = -3

Reorder the terms:
(-3 + 2x)(2 + 3x) + -6(x + -2)(x + 3) = -3

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

Combine like terms: -9x + 4x = -5x
(-6 + -5x + 6x2) + -6(x + -2)(x + 3) = -3

Reorder the terms:
-6 + -5x + 6x2 + -6(-2 + x)(x + 3) = -3

Reorder the terms:
-6 + -5x + 6x2 + -6(-2 + x)(3 + x) = -3

Multiply (-2 + x) * (3 + x)
-6 + -5x + 6x2 + -6(-2(3 + x) + x(3 + x)) = -3
-6 + -5x + 6x2 + -6((3 * -2 + x * -2) + x(3 + x)) = -3
-6 + -5x + 6x2 + -6((-6 + -2x) + x(3 + x)) = -3
-6 + -5x + 6x2 + -6(-6 + -2x + (3 * x + x * x)) = -3
-6 + -5x + 6x2 + -6(-6 + -2x + (3x + x2)) = -3

Combine like terms: -2x + 3x = 1x
-6 + -5x + 6x2 + -6(-6 + 1x + x2) = -3
-6 + -5x + 6x2 + (-6 * -6 + 1x * -6 + x2 * -6) = -3
-6 + -5x + 6x2 + (36 + -6x + -6x2) = -3

Reorder the terms:
-6 + 36 + -5x + -6x + 6x2 + -6x2 = -3

Combine like terms: -6 + 36 = 30
30 + -5x + -6x + 6x2 + -6x2 = -3

Combine like terms: -5x + -6x = -11x
30 + -11x + 6x2 + -6x2 = -3

Combine like terms: 6x2 + -6x2 = 0
30 + -11x + 0 = -3
30 + -11x = -3

Solving
30 + -11x = -3

Solving for variable 'x'.

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

Add '-30' to each side of the equation.
30 + -30 + -11x = -3 + -30

Combine like terms: 30 + -30 = 0
0 + -11x = -3 + -30
-11x = -3 + -30

Combine like terms: -3 + -30 = -33
-11x = -33

Divide each side by '-11'.
x = 3

Simplifying
x = 3

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