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

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


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

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

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

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

Solving for variable 'x'.

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

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

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

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

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


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

Simplifying
-2 + x = 0

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

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

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

Simplifying
x = 2

Subproblem 2
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
Solution
x = {2, 0.3333333333}

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