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

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


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

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

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

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

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

Reorder the terms:
6 + 5x + x2 = (3 + x)(5x + 1)

Reorder the terms:
6 + 5x + x2 = (3 + x)(1 + 5x)

Multiply (3 + x) * (1 + 5x)
6 + 5x + x2 = (3(1 + 5x) + x(1 + 5x))
6 + 5x + x2 = ((1 * 3 + 5x * 3) + x(1 + 5x))
6 + 5x + x2 = ((3 + 15x) + x(1 + 5x))
6 + 5x + x2 = (3 + 15x + (1 * x + 5x * x))
6 + 5x + x2 = (3 + 15x + (1x + 5x2))

Combine like terms: 15x + 1x = 16x
6 + 5x + x2 = (3 + 16x + 5x2)

Solving
6 + 5x + x2 = 3 + 16x + 5x2

Solving for variable 'x'.

Reorder the terms:
6 + -3 + 5x + -16x + x2 + -5x2 = 3 + 16x + 5x2 + -3 + -16x + -5x2

Combine like terms: 6 + -3 = 3
3 + 5x + -16x + x2 + -5x2 = 3 + 16x + 5x2 + -3 + -16x + -5x2

Combine like terms: 5x + -16x = -11x
3 + -11x + x2 + -5x2 = 3 + 16x + 5x2 + -3 + -16x + -5x2

Combine like terms: x2 + -5x2 = -4x2
3 + -11x + -4x2 = 3 + 16x + 5x2 + -3 + -16x + -5x2

Reorder the terms:
3 + -11x + -4x2 = 3 + -3 + 16x + -16x + 5x2 + -5x2

Combine like terms: 3 + -3 = 0
3 + -11x + -4x2 = 0 + 16x + -16x + 5x2 + -5x2
3 + -11x + -4x2 = 16x + -16x + 5x2 + -5x2

Combine like terms: 16x + -16x = 0
3 + -11x + -4x2 = 0 + 5x2 + -5x2
3 + -11x + -4x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
3 + -11x + -4x2 = 0

Factor a trinomial.
(1 + -4x)(3 + x) = 0


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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {0.25, -3}

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