x(5x+12)=2x^2-2x+49

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Solution for x(5x+12)=2x^2-2x+49 equation: 


Simplifying
x(5x + 12) = 2x2 + -2x + 49

Reorder the terms:
x(12 + 5x) = 2x2 + -2x + 49
(12 * x + 5x * x) = 2x2 + -2x + 49
(12x + 5x2) = 2x2 + -2x + 49

Reorder the terms:
12x + 5x2 = 49 + -2x + 2x2

Solving
12x + 5x2 = 49 + -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
-49 + 12x + 2x + 5x2 + -2x2 = 49 + -2x + 2x2 + -49 + 2x + -2x2

Combine like terms: 12x + 2x = 14x
-49 + 14x + 5x2 + -2x2 = 49 + -2x + 2x2 + -49 + 2x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-49 + 14x + 3x2 = 49 + -2x + 2x2 + -49 + 2x + -2x2

Reorder the terms:
-49 + 14x + 3x2 = 49 + -49 + -2x + 2x + 2x2 + -2x2

Combine like terms: 49 + -49 = 0
-49 + 14x + 3x2 = 0 + -2x + 2x + 2x2 + -2x2
-49 + 14x + 3x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
-49 + 14x + 3x2 = 0 + 2x2 + -2x2
-49 + 14x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-49 + 14x + 3x2 = 0

Factor a trinomial.
(-7 + -1x)(7 + -3x) = 0


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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-7, 2.333333333}

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