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

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


Simplifying
3x(1 + 5x) = 2(x + 1)
(1 * 3x + 5x * 3x) = 2(x + 1)
(3x + 15x2) = 2(x + 1)

Reorder the terms:
3x + 15x2 = 2(1 + x)
3x + 15x2 = (1 * 2 + x * 2)
3x + 15x2 = (2 + 2x)

Solving
3x + 15x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
-2 + 3x + -2x + 15x2 = 2 + 2x + -2 + -2x

Combine like terms: 3x + -2x = 1x
-2 + 1x + 15x2 = 2 + 2x + -2 + -2x

Reorder the terms:
-2 + 1x + 15x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
-2 + 1x + 15x2 = 0 + 2x + -2x
-2 + 1x + 15x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-2 + 1x + 15x2 = 0

Factor a trinomial.
(-2 + -5x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 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 + -5x = 0 + 2

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

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

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

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 = {-0.4, 0.3333333333}

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