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

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


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

Reorder the terms:
3x(1 + 2x) = (5x + 3)(2x + 1)
(1 * 3x + 2x * 3x) = (5x + 3)(2x + 1)
(3x + 6x2) = (5x + 3)(2x + 1)

Reorder the terms:
3x + 6x2 = (3 + 5x)(2x + 1)

Reorder the terms:
3x + 6x2 = (3 + 5x)(1 + 2x)

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

Combine like terms: 6x + 5x = 11x
3x + 6x2 = (3 + 11x + 10x2)

Solving
3x + 6x2 = 3 + 11x + 10x2

Solving for variable 'x'.

Reorder the terms:
-3 + 3x + -11x + 6x2 + -10x2 = 3 + 11x + 10x2 + -3 + -11x + -10x2

Combine like terms: 3x + -11x = -8x
-3 + -8x + 6x2 + -10x2 = 3 + 11x + 10x2 + -3 + -11x + -10x2

Combine like terms: 6x2 + -10x2 = -4x2
-3 + -8x + -4x2 = 3 + 11x + 10x2 + -3 + -11x + -10x2

Reorder the terms:
-3 + -8x + -4x2 = 3 + -3 + 11x + -11x + 10x2 + -10x2

Combine like terms: 3 + -3 = 0
-3 + -8x + -4x2 = 0 + 11x + -11x + 10x2 + -10x2
-3 + -8x + -4x2 = 11x + -11x + 10x2 + -10x2

Combine like terms: 11x + -11x = 0
-3 + -8x + -4x2 = 0 + 10x2 + -10x2
-3 + -8x + -4x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-3 + -8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 8x + 4x2) = 0

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

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

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

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
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
Solution
x = {-1.5, -0.5}

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