403=x(2x+5)

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Solution for 403=x(2x+5) equation: 


Simplifying
403 = x(2x + 5)

Reorder the terms:
403 = x(5 + 2x)
403 = (5 * x + 2x * x)
403 = (5x + 2x2)

Solving
403 = 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
403 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
403 + -5x + -2x2 = 0 + 2x2 + -2x2
403 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
403 + -5x + -2x2 = 0

Factor a trinomial.
(13 + -1x)(31 + 2x) = 0


Subproblem 1
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13

Subproblem 2
Set the factor '(31 + 2x)' equal to zero and attempt to solve:

Simplifying
31 + 2x = 0

Solving
31 + 2x = 0

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

Add '-31' to each side of the equation.
31 + -31 + 2x = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 2x = 0 + -31
2x = 0 + -31

Combine like terms: 0 + -31 = -31
2x = -31

Divide each side by '2'.
x = -15.5

Simplifying
x = -15.5
Solution
x = {13, -15.5}

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