(x-2)(x+3)=(x+6)(x-9)+21

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Solution for (x-2)(x+3)=(x+6)(x-9)+21 equation: 


Simplifying
(x + -2)(x + 3) = (x + 6)(x + -9) + 21

Reorder the terms:
(-2 + x)(x + 3) = (x + 6)(x + -9) + 21

Reorder the terms:
(-2 + x)(3 + x) = (x + 6)(x + -9) + 21

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = (x + 6)(x + -9) + 21
((3 * -2 + x * -2) + x(3 + x)) = (x + 6)(x + -9) + 21
((-6 + -2x) + x(3 + x)) = (x + 6)(x + -9) + 21
(-6 + -2x + (3 * x + x * x)) = (x + 6)(x + -9) + 21
(-6 + -2x + (3x + x2)) = (x + 6)(x + -9) + 21

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) = (x + 6)(x + -9) + 21

Reorder the terms:
-6 + 1x + x2 = (6 + x)(x + -9) + 21

Reorder the terms:
-6 + 1x + x2 = (6 + x)(-9 + x) + 21

Multiply (6 + x) * (-9 + x)
-6 + 1x + x2 = (6(-9 + x) + x(-9 + x)) + 21
-6 + 1x + x2 = ((-9 * 6 + x * 6) + x(-9 + x)) + 21
-6 + 1x + x2 = ((-54 + 6x) + x(-9 + x)) + 21
-6 + 1x + x2 = (-54 + 6x + (-9 * x + x * x)) + 21
-6 + 1x + x2 = (-54 + 6x + (-9x + x2)) + 21

Combine like terms: 6x + -9x = -3x
-6 + 1x + x2 = (-54 + -3x + x2) + 21

Reorder the terms:
-6 + 1x + x2 = -54 + 21 + -3x + x2

Combine like terms: -54 + 21 = -33
-6 + 1x + x2 = -33 + -3x + x2

Add '-1x2' to each side of the equation.
-6 + 1x + x2 + -1x2 = -33 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 1x + 0 = -33 + -3x + x2 + -1x2
-6 + 1x = -33 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 1x = -33 + -3x + 0
-6 + 1x = -33 + -3x

Solving
-6 + 1x = -33 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-6 + 1x + 3x = -33 + -3x + 3x

Combine like terms: 1x + 3x = 4x
-6 + 4x = -33 + -3x + 3x

Combine like terms: -3x + 3x = 0
-6 + 4x = -33 + 0
-6 + 4x = -33

Add '6' to each side of the equation.
-6 + 6 + 4x = -33 + 6

Combine like terms: -6 + 6 = 0
0 + 4x = -33 + 6
4x = -33 + 6

Combine like terms: -33 + 6 = -27
4x = -27

Divide each side by '4'.
x = -6.75

Simplifying
x = -6.75

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