(x+4)*(2x+1)=(x+1)*(8x+2)

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


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

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

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

Multiply (4 + x) * (1 + 2x)
(4(1 + 2x) + x(1 + 2x)) = (x + 1)(8x + 2)
((1 * 4 + 2x * 4) + x(1 + 2x)) = (x + 1)(8x + 2)
((4 + 8x) + x(1 + 2x)) = (x + 1)(8x + 2)
(4 + 8x + (1 * x + 2x * x)) = (x + 1)(8x + 2)
(4 + 8x + (1x + 2x2)) = (x + 1)(8x + 2)

Combine like terms: 8x + 1x = 9x
(4 + 9x + 2x2) = (x + 1)(8x + 2)

Reorder the terms:
4 + 9x + 2x2 = (1 + x)(8x + 2)

Reorder the terms:
4 + 9x + 2x2 = (1 + x)(2 + 8x)

Multiply (1 + x) * (2 + 8x)
4 + 9x + 2x2 = (1(2 + 8x) + x(2 + 8x))
4 + 9x + 2x2 = ((2 * 1 + 8x * 1) + x(2 + 8x))
4 + 9x + 2x2 = ((2 + 8x) + x(2 + 8x))
4 + 9x + 2x2 = (2 + 8x + (2 * x + 8x * x))
4 + 9x + 2x2 = (2 + 8x + (2x + 8x2))

Combine like terms: 8x + 2x = 10x
4 + 9x + 2x2 = (2 + 10x + 8x2)

Solving
4 + 9x + 2x2 = 2 + 10x + 8x2

Solving for variable 'x'.

Reorder the terms:
4 + -2 + 9x + -10x + 2x2 + -8x2 = 2 + 10x + 8x2 + -2 + -10x + -8x2

Combine like terms: 4 + -2 = 2
2 + 9x + -10x + 2x2 + -8x2 = 2 + 10x + 8x2 + -2 + -10x + -8x2

Combine like terms: 9x + -10x = -1x
2 + -1x + 2x2 + -8x2 = 2 + 10x + 8x2 + -2 + -10x + -8x2

Combine like terms: 2x2 + -8x2 = -6x2
2 + -1x + -6x2 = 2 + 10x + 8x2 + -2 + -10x + -8x2

Reorder the terms:
2 + -1x + -6x2 = 2 + -2 + 10x + -10x + 8x2 + -8x2

Combine like terms: 2 + -2 = 0
2 + -1x + -6x2 = 0 + 10x + -10x + 8x2 + -8x2
2 + -1x + -6x2 = 10x + -10x + 8x2 + -8x2

Combine like terms: 10x + -10x = 0
2 + -1x + -6x2 = 0 + 8x2 + -8x2
2 + -1x + -6x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
2 + -1x + -6x2 = 0

Factor a trinomial.
(1 + -2x)(2 + 3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0.5, -0.6666666667}

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