6x(x+1)+3=5x(x+2)

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Solution for 6x(x+1)+3=5x(x+2) equation: 


Simplifying
6x(x + 1) + 3 = 5x(x + 2)

Reorder the terms:
6x(1 + x) + 3 = 5x(x + 2)
(1 * 6x + x * 6x) + 3 = 5x(x + 2)
(6x + 6x2) + 3 = 5x(x + 2)

Reorder the terms:
3 + 6x + 6x2 = 5x(x + 2)

Reorder the terms:
3 + 6x + 6x2 = 5x(2 + x)
3 + 6x + 6x2 = (2 * 5x + x * 5x)
3 + 6x + 6x2 = (10x + 5x2)

Solving
3 + 6x + 6x2 = 10x + 5x2

Solving for variable 'x'.

Reorder the terms:
3 + 6x + -10x + 6x2 + -5x2 = 10x + 5x2 + -10x + -5x2

Combine like terms: 6x + -10x = -4x
3 + -4x + 6x2 + -5x2 = 10x + 5x2 + -10x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
3 + -4x + 1x2 = 10x + 5x2 + -10x + -5x2

Reorder the terms:
3 + -4x + 1x2 = 10x + -10x + 5x2 + -5x2

Combine like terms: 10x + -10x = 0
3 + -4x + 1x2 = 0 + 5x2 + -5x2
3 + -4x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
3 + -4x + 1x2 = 0

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


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

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}

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