(4x+1)(x+2)-2x(2x+3)=0

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Solution for (4x+1)(x+2)-2x(2x+3)=0 equation:


Simplifying
(4x + 1)(x + 2) + -2x(2x + 3) = 0

Reorder the terms:
(1 + 4x)(x + 2) + -2x(2x + 3) = 0

Reorder the terms:
(1 + 4x)(2 + x) + -2x(2x + 3) = 0

Multiply (1 + 4x) * (2 + x)
(1(2 + x) + 4x * (2 + x)) + -2x(2x + 3) = 0
((2 * 1 + x * 1) + 4x * (2 + x)) + -2x(2x + 3) = 0
((2 + 1x) + 4x * (2 + x)) + -2x(2x + 3) = 0
(2 + 1x + (2 * 4x + x * 4x)) + -2x(2x + 3) = 0
(2 + 1x + (8x + 4x2)) + -2x(2x + 3) = 0

Combine like terms: 1x + 8x = 9x
(2 + 9x + 4x2) + -2x(2x + 3) = 0

Reorder the terms:
2 + 9x + 4x2 + -2x(3 + 2x) = 0
2 + 9x + 4x2 + (3 * -2x + 2x * -2x) = 0
2 + 9x + 4x2 + (-6x + -4x2) = 0

Reorder the terms:
2 + 9x + -6x + 4x2 + -4x2 = 0

Combine like terms: 9x + -6x = 3x
2 + 3x + 4x2 + -4x2 = 0

Combine like terms: 4x2 + -4x2 = 0
2 + 3x + 0 = 0
2 + 3x = 0

Solving
2 + 3x = 0

Solving for variable 'x'.

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

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