1.5(x+3)=0.5x(x-1)

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Solution for 1.5(x+3)=0.5x(x-1) equation:


Simplifying
1.5(x + 3) = 0.5x(x + -1)

Reorder the terms:
1.5(3 + x) = 0.5x(x + -1)
(3 * 1.5 + x * 1.5) = 0.5x(x + -1)
(4.5 + 1.5x) = 0.5x(x + -1)

Reorder the terms:
4.5 + 1.5x = 0.5x(-1 + x)
4.5 + 1.5x = (-1 * 0.5x + x * 0.5x)
4.5 + 1.5x = (-0.5x + 0.5x2)

Solving
4.5 + 1.5x = -0.5x + 0.5x2

Solving for variable 'x'.

Combine like terms: 1.5x + 0.5x = 2x
4.5 + 2x + -0.5x2 = -0.5x + 0.5x2 + 0.5x + -0.5x2

Reorder the terms:
4.5 + 2x + -0.5x2 = -0.5x + 0.5x + 0.5x2 + -0.5x2

Combine like terms: -0.5x + 0.5x = 0.0
4.5 + 2x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2
4.5 + 2x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
4.5 + 2x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-9 + -4x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -4x + 9 + x2 = 0 + 9

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

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

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

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 9 + 4

Reorder the terms:
4 + -4x + x2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + -4x + x2 = 13

Factor a perfect square on the left side:
(x + -2)(x + -2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -2) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + -2 = 3.605551275 Simplifying x + -2 = 3.605551275 Reorder the terms: -2 + x = 3.605551275 Solving -2 + x = 3.605551275 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 + x = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.605551275 + 2 x = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 x = 5.605551275 Simplifying x = 5.605551275

Subproblem 2

x + -2 = -3.605551275 Simplifying x + -2 = -3.605551275 Reorder the terms: -2 + x = -3.605551275 Solving -2 + x = -3.605551275 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 + x = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.605551275 + 2 x = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 x = -1.605551275 Simplifying x = -1.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.605551275, -1.605551275}

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