13x-2x(x+4)=8x+1

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Solution for 13x-2x(x+4)=8x+1 equation: 


Simplifying
13x + -2x(x + 4) = 8x + 1

Reorder the terms:
13x + -2x(4 + x) = 8x + 1
13x + (4 * -2x + x * -2x) = 8x + 1
13x + (-8x + -2x2) = 8x + 1

Combine like terms: 13x + -8x = 5x
5x + -2x2 = 8x + 1

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

Solving
5x + -2x2 = 1 + 8x

Solving for variable 'x'.

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

Combine like terms: 5x + -8x = -3x
-1 + -3x + -2x2 = 1 + 8x + -1 + -8x

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

Combine like terms: 1 + -1 = 0
-1 + -3x + -2x2 = 0 + 8x + -8x
-1 + -3x + -2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-1 + -3x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 3x + 2x2) = 0

Factor a trinomial.
-1((1 + x)(1 + 2x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1, -0.5}

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