x(5x+2)=2x^2-3x+12

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Solution for x(5x+2)=2x^2-3x+12 equation: 


Simplifying
x(5x + 2) = 2x2 + -3x + 12

Reorder the terms:
x(2 + 5x) = 2x2 + -3x + 12
(2 * x + 5x * x) = 2x2 + -3x + 12
(2x + 5x2) = 2x2 + -3x + 12

Reorder the terms:
2x + 5x2 = 12 + -3x + 2x2

Solving
2x + 5x2 = 12 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-12 + 2x + 3x + 5x2 + -2x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2

Combine like terms: 2x + 3x = 5x
-12 + 5x + 5x2 + -2x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-12 + 5x + 3x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2

Reorder the terms:
-12 + 5x + 3x2 = 12 + -12 + -3x + 3x + 2x2 + -2x2

Combine like terms: 12 + -12 = 0
-12 + 5x + 3x2 = 0 + -3x + 3x + 2x2 + -2x2
-12 + 5x + 3x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-12 + 5x + 3x2 = 0 + 2x2 + -2x2
-12 + 5x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + 5x + 3x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-3, 1.333333333}

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