(2x+1)(3x+2)=5x(x+1)+1

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


Simplifying
(2x + 1)(3x + 2) = 5x(x + 1) + 1

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

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

Multiply (1 + 2x) * (2 + 3x)
(1(2 + 3x) + 2x * (2 + 3x)) = 5x(x + 1) + 1
((2 * 1 + 3x * 1) + 2x * (2 + 3x)) = 5x(x + 1) + 1
((2 + 3x) + 2x * (2 + 3x)) = 5x(x + 1) + 1
(2 + 3x + (2 * 2x + 3x * 2x)) = 5x(x + 1) + 1
(2 + 3x + (4x + 6x2)) = 5x(x + 1) + 1

Combine like terms: 3x + 4x = 7x
(2 + 7x + 6x2) = 5x(x + 1) + 1

Reorder the terms:
2 + 7x + 6x2 = 5x(1 + x) + 1
2 + 7x + 6x2 = (1 * 5x + x * 5x) + 1
2 + 7x + 6x2 = (5x + 5x2) + 1

Reorder the terms:
2 + 7x + 6x2 = 1 + 5x + 5x2

Solving
2 + 7x + 6x2 = 1 + 5x + 5x2

Solving for variable 'x'.

Reorder the terms:
2 + -1 + 7x + -5x + 6x2 + -5x2 = 1 + 5x + 5x2 + -1 + -5x + -5x2

Combine like terms: 2 + -1 = 1
1 + 7x + -5x + 6x2 + -5x2 = 1 + 5x + 5x2 + -1 + -5x + -5x2

Combine like terms: 7x + -5x = 2x
1 + 2x + 6x2 + -5x2 = 1 + 5x + 5x2 + -1 + -5x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
1 + 2x + 1x2 = 1 + 5x + 5x2 + -1 + -5x + -5x2

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

Combine like terms: 1 + -1 = 0
1 + 2x + 1x2 = 0 + 5x + -5x + 5x2 + -5x2
1 + 2x + 1x2 = 5x + -5x + 5x2 + -5x2

Combine like terms: 5x + -5x = 0
1 + 2x + 1x2 = 0 + 5x2 + -5x2
1 + 2x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
1 + 2x + 1x2 = 0

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


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 + 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
Solution
x = {-1, -1}

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