x(2x+1)=5x+2x

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Solution for x(2x+1)=5x+2x equation:


Simplifying
x(2x + 1) = 5x + 2x

Reorder the terms:
x(1 + 2x) = 5x + 2x
(1 * x + 2x * x) = 5x + 2x
(1x + 2x2) = 5x + 2x

Combine like terms: 5x + 2x = 7x
1x + 2x2 = 7x

Solving
1x + 2x2 = 7x

Solving for variable 'x'.

Reorder the terms:
1x + -7x + 2x2 = 7x + -7x

Combine like terms: 1x + -7x = -6x
-6x + 2x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-6x + 2x2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

Simplifying
x = 3
Solution
x = {0, 3}

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