2x^2-(x-3)(x-5)=8x+1

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Solution for 2x^2-(x-3)(x-5)=8x+1 equation: 


Simplifying
2x2 + -1(x + -3)(x + -5) = 8x + 1

Reorder the terms:
2x2 + -1(-3 + x)(x + -5) = 8x + 1

Reorder the terms:
2x2 + -1(-3 + x)(-5 + x) = 8x + 1

Multiply (-3 + x) * (-5 + x)
2x2 + -1(-3(-5 + x) + x(-5 + x)) = 8x + 1
2x2 + -1((-5 * -3 + x * -3) + x(-5 + x)) = 8x + 1
2x2 + -1((15 + -3x) + x(-5 + x)) = 8x + 1
2x2 + -1(15 + -3x + (-5 * x + x * x)) = 8x + 1
2x2 + -1(15 + -3x + (-5x + x2)) = 8x + 1

Combine like terms: -3x + -5x = -8x
2x2 + -1(15 + -8x + x2) = 8x + 1
2x2 + (15 * -1 + -8x * -1 + x2 * -1) = 8x + 1
2x2 + (-15 + 8x + -1x2) = 8x + 1

Reorder the terms:
-15 + 8x + 2x2 + -1x2 = 8x + 1

Combine like terms: 2x2 + -1x2 = 1x2
-15 + 8x + 1x2 = 8x + 1

Reorder the terms:
-15 + 8x + 1x2 = 1 + 8x

Add '-8x' to each side of the equation.
-15 + 8x + -8x + 1x2 = 1 + 8x + -8x

Combine like terms: 8x + -8x = 0
-15 + 0 + 1x2 = 1 + 8x + -8x
-15 + 1x2 = 1 + 8x + -8x

Combine like terms: 8x + -8x = 0
-15 + 1x2 = 1 + 0
-15 + 1x2 = 1

Solving
-15 + 1x2 = 1

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + 1x2 = 1 + 15

Combine like terms: -15 + 15 = 0
0 + 1x2 = 1 + 15
1x2 = 1 + 15

Combine like terms: 1 + 15 = 16
1x2 = 16

Divide each side by '1'.
x2 = 16

Simplifying
x2 = 16

Take the square root of each side:
x = {-4, 4}

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