3x(2x+3)=2x(x+4.5)+2

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Solution for 3x(2x+3)=2x(x+4.5)+2 equation: 


Simplifying
3x(2x + 3) = 2x(x + 4.5) + 2

Reorder the terms:
3x(3 + 2x) = 2x(x + 4.5) + 2
(3 * 3x + 2x * 3x) = 2x(x + 4.5) + 2
(9x + 6x2) = 2x(x + 4.5) + 2

Reorder the terms:
9x + 6x2 = 2x(4.5 + x) + 2
9x + 6x2 = (4.5 * 2x + x * 2x) + 2
9x + 6x2 = (9x + 2x2) + 2

Reorder the terms:
9x + 6x2 = 2 + 9x + 2x2

Add '-9x' to each side of the equation.
9x + -9x + 6x2 = 2 + 9x + -9x + 2x2

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

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

Solving
6x2 = 2 + 2x2

Solving for variable 'x'.

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

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

Combine like terms: 6x2 + -2x2 = 4x2
4x2 = 2 + 2x2 + -2x2

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

Divide each side by '4'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}

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