x(3x+5)=x(x+2)+14

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Solution for x(3x+5)=x(x+2)+14 equation: 


Simplifying
x(3x + 5) = x(x + 2) + 14

Reorder the terms:
x(5 + 3x) = x(x + 2) + 14
(5 * x + 3x * x) = x(x + 2) + 14
(5x + 3x2) = x(x + 2) + 14

Reorder the terms:
5x + 3x2 = x(2 + x) + 14
5x + 3x2 = (2 * x + x * x) + 14
5x + 3x2 = (2x + x2) + 14

Reorder the terms:
5x + 3x2 = 14 + 2x + x2

Solving
5x + 3x2 = 14 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-14 + 5x + -2x + 3x2 + -1x2 = 14 + 2x + x2 + -14 + -2x + -1x2

Combine like terms: 5x + -2x = 3x
-14 + 3x + 3x2 + -1x2 = 14 + 2x + x2 + -14 + -2x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-14 + 3x + 2x2 = 14 + 2x + x2 + -14 + -2x + -1x2

Reorder the terms:
-14 + 3x + 2x2 = 14 + -14 + 2x + -2x + x2 + -1x2

Combine like terms: 14 + -14 = 0
-14 + 3x + 2x2 = 0 + 2x + -2x + x2 + -1x2
-14 + 3x + 2x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-14 + 3x + 2x2 = 0 + x2 + -1x2
-14 + 3x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + 3x + 2x2 = 0

Factor a trinomial.
(-7 + -2x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

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

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

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, 2}

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