(2x+1)(3x+5)=20x+3

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Solution for (2x+1)(3x+5)=20x+3 equation: 


Simplifying
(2x + 1)(3x + 5) = 20x + 3

Reorder the terms:
(1 + 2x)(3x + 5) = 20x + 3

Reorder the terms:
(1 + 2x)(5 + 3x) = 20x + 3

Multiply (1 + 2x) * (5 + 3x)
(1(5 + 3x) + 2x * (5 + 3x)) = 20x + 3
((5 * 1 + 3x * 1) + 2x * (5 + 3x)) = 20x + 3
((5 + 3x) + 2x * (5 + 3x)) = 20x + 3
(5 + 3x + (5 * 2x + 3x * 2x)) = 20x + 3
(5 + 3x + (10x + 6x2)) = 20x + 3

Combine like terms: 3x + 10x = 13x
(5 + 13x + 6x2) = 20x + 3

Reorder the terms:
5 + 13x + 6x2 = 3 + 20x

Solving
5 + 13x + 6x2 = 3 + 20x

Solving for variable 'x'.

Reorder the terms:
5 + -3 + 13x + -20x + 6x2 = 3 + 20x + -3 + -20x

Combine like terms: 5 + -3 = 2
2 + 13x + -20x + 6x2 = 3 + 20x + -3 + -20x

Combine like terms: 13x + -20x = -7x
2 + -7x + 6x2 = 3 + 20x + -3 + -20x

Reorder the terms:
2 + -7x + 6x2 = 3 + -3 + 20x + -20x

Combine like terms: 3 + -3 = 0
2 + -7x + 6x2 = 0 + 20x + -20x
2 + -7x + 6x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
2 + -7x + 6x2 = 0

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


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

Simplifying
1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0.5, 0.6666666667}

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