x(6x+4)=(2x+1)(2+3x)

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Solution for x(6x+4)=(2x+1)(2+3x) equation:


Simplifying
x(6x + 4) = (2x + 1)(2 + 3x)

Reorder the terms:
x(4 + 6x) = (2x + 1)(2 + 3x)
(4 * x + 6x * x) = (2x + 1)(2 + 3x)
(4x + 6x2) = (2x + 1)(2 + 3x)

Reorder the terms:
4x + 6x2 = (1 + 2x)(2 + 3x)

Multiply (1 + 2x) * (2 + 3x)
4x + 6x2 = (1(2 + 3x) + 2x * (2 + 3x))
4x + 6x2 = ((2 * 1 + 3x * 1) + 2x * (2 + 3x))
4x + 6x2 = ((2 + 3x) + 2x * (2 + 3x))
4x + 6x2 = (2 + 3x + (2 * 2x + 3x * 2x))
4x + 6x2 = (2 + 3x + (4x + 6x2))

Combine like terms: 3x + 4x = 7x
4x + 6x2 = (2 + 7x + 6x2)

Add '-6x2' to each side of the equation.
4x + 6x2 + -6x2 = 2 + 7x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
4x + 0 = 2 + 7x + 6x2 + -6x2
4x = 2 + 7x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
4x = 2 + 7x + 0
4x = 2 + 7x

Solving
4x = 2 + 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
4x + -7x = 2 + 7x + -7x

Combine like terms: 4x + -7x = -3x
-3x = 2 + 7x + -7x

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

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

Simplifying
x = -0.6666666667

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