2x(x+3)-14=x(x-2)+19

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Solution for 2x(x+3)-14=x(x-2)+19 equation: 


Simplifying
2x(x + 3) + -14 = x(x + -2) + 19

Reorder the terms:
2x(3 + x) + -14 = x(x + -2) + 19
(3 * 2x + x * 2x) + -14 = x(x + -2) + 19
(6x + 2x2) + -14 = x(x + -2) + 19

Reorder the terms:
-14 + 6x + 2x2 = x(x + -2) + 19

Reorder the terms:
-14 + 6x + 2x2 = x(-2 + x) + 19
-14 + 6x + 2x2 = (-2 * x + x * x) + 19
-14 + 6x + 2x2 = (-2x + x2) + 19

Reorder the terms:
-14 + 6x + 2x2 = 19 + -2x + x2

Solving
-14 + 6x + 2x2 = 19 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-14 + -19 + 6x + 2x + 2x2 + -1x2 = 19 + -2x + x2 + -19 + 2x + -1x2

Combine like terms: -14 + -19 = -33
-33 + 6x + 2x + 2x2 + -1x2 = 19 + -2x + x2 + -19 + 2x + -1x2

Combine like terms: 6x + 2x = 8x
-33 + 8x + 2x2 + -1x2 = 19 + -2x + x2 + -19 + 2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-33 + 8x + 1x2 = 19 + -2x + x2 + -19 + 2x + -1x2

Reorder the terms:
-33 + 8x + 1x2 = 19 + -19 + -2x + 2x + x2 + -1x2

Combine like terms: 19 + -19 = 0
-33 + 8x + 1x2 = 0 + -2x + 2x + x2 + -1x2
-33 + 8x + 1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-33 + 8x + 1x2 = 0 + x2 + -1x2
-33 + 8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-33 + 8x + 1x2 = 0

Factor a trinomial.
(-11 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-11, 3}

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