(x-5)(x+3)+(x-8)(x+10)=105

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Solution for (x-5)(x+3)+(x-8)(x+10)=105 equation: 


Simplifying
(x + -5)(x + 3) + (x + -8)(x + 10) = 105

Reorder the terms:
(-5 + x)(x + 3) + (x + -8)(x + 10) = 105

Reorder the terms:
(-5 + x)(3 + x) + (x + -8)(x + 10) = 105

Multiply (-5 + x) * (3 + x)
(-5(3 + x) + x(3 + x)) + (x + -8)(x + 10) = 105
((3 * -5 + x * -5) + x(3 + x)) + (x + -8)(x + 10) = 105
((-15 + -5x) + x(3 + x)) + (x + -8)(x + 10) = 105
(-15 + -5x + (3 * x + x * x)) + (x + -8)(x + 10) = 105
(-15 + -5x + (3x + x2)) + (x + -8)(x + 10) = 105

Combine like terms: -5x + 3x = -2x
(-15 + -2x + x2) + (x + -8)(x + 10) = 105

Reorder the terms:
-15 + -2x + x2 + (-8 + x)(x + 10) = 105

Reorder the terms:
-15 + -2x + x2 + (-8 + x)(10 + x) = 105

Multiply (-8 + x) * (10 + x)
-15 + -2x + x2 + (-8(10 + x) + x(10 + x)) = 105
-15 + -2x + x2 + ((10 * -8 + x * -8) + x(10 + x)) = 105
-15 + -2x + x2 + ((-80 + -8x) + x(10 + x)) = 105
-15 + -2x + x2 + (-80 + -8x + (10 * x + x * x)) = 105
-15 + -2x + x2 + (-80 + -8x + (10x + x2)) = 105

Combine like terms: -8x + 10x = 2x
-15 + -2x + x2 + (-80 + 2x + x2) = 105

Reorder the terms:
-15 + -80 + -2x + 2x + x2 + x2 = 105

Combine like terms: -15 + -80 = -95
-95 + -2x + 2x + x2 + x2 = 105

Combine like terms: -2x + 2x = 0
-95 + 0 + x2 + x2 = 105
-95 + x2 + x2 = 105

Combine like terms: x2 + x2 = 2x2
-95 + 2x2 = 105

Solving
-95 + 2x2 = 105

Solving for variable 'x'.

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

Add '95' to each side of the equation.
-95 + 95 + 2x2 = 105 + 95

Combine like terms: -95 + 95 = 0
0 + 2x2 = 105 + 95
2x2 = 105 + 95

Combine like terms: 105 + 95 = 200
2x2 = 200

Divide each side by '2'.
x2 = 100

Simplifying
x2 = 100

Take the square root of each side:
x = {-10, 10}

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