3x(5x+1)=13x+5

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Solution for 3x(5x+1)=13x+5 equation: 


Simplifying
3x(5x + 1) = 13x + 5

Reorder the terms:
3x(1 + 5x) = 13x + 5
(1 * 3x + 5x * 3x) = 13x + 5
(3x + 15x2) = 13x + 5

Reorder the terms:
3x + 15x2 = 5 + 13x

Solving
3x + 15x2 = 5 + 13x

Solving for variable 'x'.

Reorder the terms:
-5 + 3x + -13x + 15x2 = 5 + 13x + -5 + -13x

Combine like terms: 3x + -13x = -10x
-5 + -10x + 15x2 = 5 + 13x + -5 + -13x

Reorder the terms:
-5 + -10x + 15x2 = 5 + -5 + 13x + -13x

Combine like terms: 5 + -5 = 0
-5 + -10x + 15x2 = 0 + 13x + -13x
-5 + -10x + 15x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-5 + -10x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + -2x + 3x2) = 0

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

Ignore the factor 5.

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 '(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
Solution
x = {-0.3333333333, 1}

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