x(5x+12)=2x^2-5x+56

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Solution for x(5x+12)=2x^2-5x+56 equation: 


Simplifying
x(5x + 12) = 2x2 + -5x + 56

Reorder the terms:
x(12 + 5x) = 2x2 + -5x + 56
(12 * x + 5x * x) = 2x2 + -5x + 56
(12x + 5x2) = 2x2 + -5x + 56

Reorder the terms:
12x + 5x2 = 56 + -5x + 2x2

Solving
12x + 5x2 = 56 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-56 + 12x + 5x + 5x2 + -2x2 = 56 + -5x + 2x2 + -56 + 5x + -2x2

Combine like terms: 12x + 5x = 17x
-56 + 17x + 5x2 + -2x2 = 56 + -5x + 2x2 + -56 + 5x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-56 + 17x + 3x2 = 56 + -5x + 2x2 + -56 + 5x + -2x2

Reorder the terms:
-56 + 17x + 3x2 = 56 + -56 + -5x + 5x + 2x2 + -2x2

Combine like terms: 56 + -56 = 0
-56 + 17x + 3x2 = 0 + -5x + 5x + 2x2 + -2x2
-56 + 17x + 3x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
-56 + 17x + 3x2 = 0 + 2x2 + -2x2
-56 + 17x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-56 + 17x + 3x2 = 0

Factor a trinomial.
(-8 + -1x)(7 + -3x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

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

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

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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 = {-8, 2.333333333}

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