4(5x+1)3(8x+1)=10x+1

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Solution for 4(5x+1)3(8x+1)=10x+1 equation: 


Simplifying
4(5x + 1) * 3(8x + 1) = 10x + 1

Reorder the terms:
4(1 + 5x) * 3(8x + 1) = 10x + 1

Reorder the terms:
4(1 + 5x) * 3(1 + 8x) = 10x + 1

Reorder the terms for easier multiplication:
4 * 3(1 + 5x)(1 + 8x) = 10x + 1

Multiply 4 * 3
12(1 + 5x)(1 + 8x) = 10x + 1

Multiply (1 + 5x) * (1 + 8x)
12(1(1 + 8x) + 5x * (1 + 8x)) = 10x + 1
12((1 * 1 + 8x * 1) + 5x * (1 + 8x)) = 10x + 1
12((1 + 8x) + 5x * (1 + 8x)) = 10x + 1
12(1 + 8x + (1 * 5x + 8x * 5x)) = 10x + 1
12(1 + 8x + (5x + 40x2)) = 10x + 1

Combine like terms: 8x + 5x = 13x
12(1 + 13x + 40x2) = 10x + 1
(1 * 12 + 13x * 12 + 40x2 * 12) = 10x + 1
(12 + 156x + 480x2) = 10x + 1

Reorder the terms:
12 + 156x + 480x2 = 1 + 10x

Solving
12 + 156x + 480x2 = 1 + 10x

Solving for variable 'x'.

Reorder the terms:
12 + -1 + 156x + -10x + 480x2 = 1 + 10x + -1 + -10x

Combine like terms: 12 + -1 = 11
11 + 156x + -10x + 480x2 = 1 + 10x + -1 + -10x

Combine like terms: 156x + -10x = 146x
11 + 146x + 480x2 = 1 + 10x + -1 + -10x

Reorder the terms:
11 + 146x + 480x2 = 1 + -1 + 10x + -10x

Combine like terms: 1 + -1 = 0
11 + 146x + 480x2 = 0 + 10x + -10x
11 + 146x + 480x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
11 + 146x + 480x2 = 0

Factor a trinomial.
(1 + 6x)(11 + 80x) = 0


Subproblem 1
Set the factor '(1 + 6x)' equal to zero and attempt to solve:

Simplifying
1 + 6x = 0

Solving
1 + 6x = 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 + 6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6x = 0 + -1
6x = 0 + -1

Combine like terms: 0 + -1 = -1
6x = -1

Divide each side by '6'.
x = -0.1666666667

Simplifying
x = -0.1666666667

Subproblem 2
Set the factor '(11 + 80x)' equal to zero and attempt to solve:

Simplifying
11 + 80x = 0

Solving
11 + 80x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 80x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 80x = 0 + -11
80x = 0 + -11

Combine like terms: 0 + -11 = -11
80x = -11

Divide each side by '80'.
x = -0.1375

Simplifying
x = -0.1375
Solution
x = {-0.1666666667, -0.1375}

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