2X(X+1)=X(X+5)+3(12-X)

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Solution for 2X(X+1)=X(X+5)+3(12-X) equation: 


Simplifying
2X(X + 1) = X(X + 5) + 3(12 + -1X)

Reorder the terms:
2X(1 + X) = X(X + 5) + 3(12 + -1X)
(1 * 2X + X * 2X) = X(X + 5) + 3(12 + -1X)
(2X + 2X2) = X(X + 5) + 3(12 + -1X)

Reorder the terms:
2X + 2X2 = X(5 + X) + 3(12 + -1X)
2X + 2X2 = (5 * X + X * X) + 3(12 + -1X)
2X + 2X2 = (5X + X2) + 3(12 + -1X)
2X + 2X2 = 5X + X2 + (12 * 3 + -1X * 3)
2X + 2X2 = 5X + X2 + (36 + -3X)

Reorder the terms:
2X + 2X2 = 36 + 5X + -3X + X2

Combine like terms: 5X + -3X = 2X
2X + 2X2 = 36 + 2X + X2

Add '-2X' to each side of the equation.
2X + -2X + 2X2 = 36 + 2X + -2X + X2

Combine like terms: 2X + -2X = 0
0 + 2X2 = 36 + 2X + -2X + X2
2X2 = 36 + 2X + -2X + X2

Combine like terms: 2X + -2X = 0
2X2 = 36 + 0 + X2
2X2 = 36 + X2

Solving
2X2 = 36 + X2

Solving for variable 'X'.

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

Add '-1X2' to each side of the equation.
2X2 + -1X2 = 36 + X2 + -1X2

Combine like terms: 2X2 + -1X2 = 1X2
1X2 = 36 + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
1X2 = 36 + 0
1X2 = 36

Divide each side by '1'.
X2 = 36

Simplifying
X2 = 36

Take the square root of each side:
X = {-6, 6}

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