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

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


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

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

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

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

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

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

Solving
-2 + -3x + 2x2 = 6 + 3x

Solving for variable 'x'.

Reorder the terms:
-2 + -6 + -3x + -3x + 2x2 = 6 + 3x + -6 + -3x

Combine like terms: -2 + -6 = -8
-8 + -3x + -3x + 2x2 = 6 + 3x + -6 + -3x

Combine like terms: -3x + -3x = -6x
-8 + -6x + 2x2 = 6 + 3x + -6 + -3x

Reorder the terms:
-8 + -6x + 2x2 = 6 + -6 + 3x + -3x

Combine like terms: 6 + -6 = 0
-8 + -6x + 2x2 = 0 + 3x + -3x
-8 + -6x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-8 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -3x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}

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