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

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


Simplifying
(x + -6)(x + 3) = x(x + -2) + -1(2x + -3)

Reorder the terms:
(-6 + x)(x + 3) = x(x + -2) + -1(2x + -3)

Reorder the terms:
(-6 + x)(3 + x) = x(x + -2) + -1(2x + -3)

Multiply (-6 + x) * (3 + x)
(-6(3 + x) + x(3 + x)) = x(x + -2) + -1(2x + -3)
((3 * -6 + x * -6) + x(3 + x)) = x(x + -2) + -1(2x + -3)
((-18 + -6x) + x(3 + x)) = x(x + -2) + -1(2x + -3)
(-18 + -6x + (3 * x + x * x)) = x(x + -2) + -1(2x + -3)
(-18 + -6x + (3x + x2)) = x(x + -2) + -1(2x + -3)

Combine like terms: -6x + 3x = -3x
(-18 + -3x + x2) = x(x + -2) + -1(2x + -3)

Reorder the terms:
-18 + -3x + x2 = x(-2 + x) + -1(2x + -3)
-18 + -3x + x2 = (-2 * x + x * x) + -1(2x + -3)
-18 + -3x + x2 = (-2x + x2) + -1(2x + -3)

Reorder the terms:
-18 + -3x + x2 = -2x + x2 + -1(-3 + 2x)
-18 + -3x + x2 = -2x + x2 + (-3 * -1 + 2x * -1)
-18 + -3x + x2 = -2x + x2 + (3 + -2x)

Reorder the terms:
-18 + -3x + x2 = 3 + -2x + -2x + x2

Combine like terms: -2x + -2x = -4x
-18 + -3x + x2 = 3 + -4x + x2

Add '-1x2' to each side of the equation.
-18 + -3x + x2 + -1x2 = 3 + -4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + -3x + 0 = 3 + -4x + x2 + -1x2
-18 + -3x = 3 + -4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + -3x = 3 + -4x + 0
-18 + -3x = 3 + -4x

Solving
-18 + -3x = 3 + -4x

Solving for variable 'x'.

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

Add '4x' to each side of the equation.
-18 + -3x + 4x = 3 + -4x + 4x

Combine like terms: -3x + 4x = 1x
-18 + 1x = 3 + -4x + 4x

Combine like terms: -4x + 4x = 0
-18 + 1x = 3 + 0
-18 + 1x = 3

Add '18' to each side of the equation.
-18 + 18 + 1x = 3 + 18

Combine like terms: -18 + 18 = 0
0 + 1x = 3 + 18
1x = 3 + 18

Combine like terms: 3 + 18 = 21
1x = 21

Divide each side by '1'.
x = 21

Simplifying
x = 21

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