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

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


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

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

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

Multiply (1 + 2x) * (-3 + x)
0 = (1(-3 + x) + 2x * (-3 + x))
0 = ((-3 * 1 + x * 1) + 2x * (-3 + x))
0 = ((-3 + 1x) + 2x * (-3 + x))
0 = (-3 + 1x + (-3 * 2x + x * 2x))
0 = (-3 + 1x + (-6x + 2x2))

Combine like terms: 1x + -6x = -5x
0 = (-3 + -5x + 2x2)

Solving
0 = -3 + -5x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + 5x + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2

Reorder the terms:
3 + 5x + -2x2 = -3 + 3 + -5x + 5x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
3 + 5x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2
3 + 5x + -2x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
3 + 5x + -2x2 = 0 + 2x2 + -2x2
3 + 5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 5x + -2x2 = 0

Factor a trinomial.
(3 + -1x)(1 + 2x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {3, -0.5}

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