(x+10)(x-5)-(x-6)(x+3)=16

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Solution for (x+10)(x-5)-(x-6)(x+3)=16 equation:


Simplifying
(x + 10)(x + -5) + -1(x + -6)(x + 3) = 16

Reorder the terms:
(10 + x)(x + -5) + -1(x + -6)(x + 3) = 16

Reorder the terms:
(10 + x)(-5 + x) + -1(x + -6)(x + 3) = 16

Multiply (10 + x) * (-5 + x)
(10(-5 + x) + x(-5 + x)) + -1(x + -6)(x + 3) = 16
((-5 * 10 + x * 10) + x(-5 + x)) + -1(x + -6)(x + 3) = 16
((-50 + 10x) + x(-5 + x)) + -1(x + -6)(x + 3) = 16
(-50 + 10x + (-5 * x + x * x)) + -1(x + -6)(x + 3) = 16
(-50 + 10x + (-5x + x2)) + -1(x + -6)(x + 3) = 16

Combine like terms: 10x + -5x = 5x
(-50 + 5x + x2) + -1(x + -6)(x + 3) = 16

Reorder the terms:
-50 + 5x + x2 + -1(-6 + x)(x + 3) = 16

Reorder the terms:
-50 + 5x + x2 + -1(-6 + x)(3 + x) = 16

Multiply (-6 + x) * (3 + x)
-50 + 5x + x2 + -1(-6(3 + x) + x(3 + x)) = 16
-50 + 5x + x2 + -1((3 * -6 + x * -6) + x(3 + x)) = 16
-50 + 5x + x2 + -1((-18 + -6x) + x(3 + x)) = 16
-50 + 5x + x2 + -1(-18 + -6x + (3 * x + x * x)) = 16
-50 + 5x + x2 + -1(-18 + -6x + (3x + x2)) = 16

Combine like terms: -6x + 3x = -3x
-50 + 5x + x2 + -1(-18 + -3x + x2) = 16
-50 + 5x + x2 + (-18 * -1 + -3x * -1 + x2 * -1) = 16
-50 + 5x + x2 + (18 + 3x + -1x2) = 16

Reorder the terms:
-50 + 18 + 5x + 3x + x2 + -1x2 = 16

Combine like terms: -50 + 18 = -32
-32 + 5x + 3x + x2 + -1x2 = 16

Combine like terms: 5x + 3x = 8x
-32 + 8x + x2 + -1x2 = 16

Combine like terms: x2 + -1x2 = 0
-32 + 8x + 0 = 16
-32 + 8x = 16

Solving
-32 + 8x = 16

Solving for variable 'x'.

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

Add '32' to each side of the equation.
-32 + 32 + 8x = 16 + 32

Combine like terms: -32 + 32 = 0
0 + 8x = 16 + 32
8x = 16 + 32

Combine like terms: 16 + 32 = 48
8x = 48

Divide each side by '8'.
x = 6

Simplifying
x = 6

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