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

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


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

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

Reorder the terms:
3x + 3x2 = 2(-1 + 5x)
3x + 3x2 = (-1 * 2 + 5x * 2)
3x + 3x2 = (-2 + 10x)

Solving
3x + 3x2 = -2 + 10x

Solving for variable 'x'.

Reorder the terms:
2 + 3x + -10x + 3x2 = -2 + 10x + 2 + -10x

Combine like terms: 3x + -10x = -7x
2 + -7x + 3x2 = -2 + 10x + 2 + -10x

Reorder the terms:
2 + -7x + 3x2 = -2 + 2 + 10x + -10x

Combine like terms: -2 + 2 = 0
2 + -7x + 3x2 = 0 + 10x + -10x
2 + -7x + 3x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
2 + -7x + 3x2 = 0

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


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

Simplifying
1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.3333333333, 2}

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