x(2x+1)=3x+4

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Solution for x(2x+1)=3x+4 equation: 


Simplifying
x(2x + 1) = 3x + 4

Reorder the terms:
x(1 + 2x) = 3x + 4
(1 * x + 2x * x) = 3x + 4
(1x + 2x2) = 3x + 4

Reorder the terms:
1x + 2x2 = 4 + 3x

Solving
1x + 2x2 = 4 + 3x

Solving for variable 'x'.

Reorder the terms:
-4 + 1x + -3x + 2x2 = 4 + 3x + -4 + -3x

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

Reorder the terms:
-4 + -2x + 2x2 = 4 + -4 + 3x + -3x

Combine like terms: 4 + -4 = 0
-4 + -2x + 2x2 = 0 + 3x + -3x
-4 + -2x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-4 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -1x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}

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