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

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


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

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

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

Multiply (1 + 8x) * (-2 + x)
(1(-2 + x) + 8x * (-2 + x)) = 13 + -1x
((-2 * 1 + x * 1) + 8x * (-2 + x)) = 13 + -1x
((-2 + 1x) + 8x * (-2 + x)) = 13 + -1x
(-2 + 1x + (-2 * 8x + x * 8x)) = 13 + -1x
(-2 + 1x + (-16x + 8x2)) = 13 + -1x

Combine like terms: 1x + -16x = -15x
(-2 + -15x + 8x2) = 13 + -1x

Solving
-2 + -15x + 8x2 = 13 + -1x

Solving for variable 'x'.

Reorder the terms:
-2 + -13 + -15x + x + 8x2 = 13 + -1x + -13 + x

Combine like terms: -2 + -13 = -15
-15 + -15x + x + 8x2 = 13 + -1x + -13 + x

Combine like terms: -15x + x = -14x
-15 + -14x + 8x2 = 13 + -1x + -13 + x

Reorder the terms:
-15 + -14x + 8x2 = 13 + -13 + -1x + x

Combine like terms: 13 + -13 = 0
-15 + -14x + 8x2 = 0 + -1x + x
-15 + -14x + 8x2 = -1x + x

Combine like terms: -1x + x = 0
-15 + -14x + 8x2 = 0

Factor a trinomial.
(-3 + -4x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.75, 2.5}

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