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

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Solution for (x-1)(x+6)-(x-2)(x-3)=3 equation: 


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

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

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

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

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

Reorder the terms:
-6 + 5x + x2 + -1(-2 + x)(x + -3) = 3

Reorder the terms:
-6 + 5x + x2 + -1(-2 + x)(-3 + x) = 3

Multiply (-2 + x) * (-3 + x)
-6 + 5x + x2 + -1(-2(-3 + x) + x(-3 + x)) = 3
-6 + 5x + x2 + -1((-3 * -2 + x * -2) + x(-3 + x)) = 3
-6 + 5x + x2 + -1((6 + -2x) + x(-3 + x)) = 3
-6 + 5x + x2 + -1(6 + -2x + (-3 * x + x * x)) = 3
-6 + 5x + x2 + -1(6 + -2x + (-3x + x2)) = 3

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

Reorder the terms:
-6 + -6 + 5x + 5x + x2 + -1x2 = 3

Combine like terms: -6 + -6 = -12
-12 + 5x + 5x + x2 + -1x2 = 3

Combine like terms: 5x + 5x = 10x
-12 + 10x + x2 + -1x2 = 3

Combine like terms: x2 + -1x2 = 0
-12 + 10x + 0 = 3
-12 + 10x = 3

Solving
-12 + 10x = 3

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + 10x = 3 + 12

Combine like terms: -12 + 12 = 0
0 + 10x = 3 + 12
10x = 3 + 12

Combine like terms: 3 + 12 = 15
10x = 15

Divide each side by '10'.
x = 1.5

Simplifying
x = 1.5

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