2x(x+4)+x^2-3(4x-7)x=6x^2+12

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Solution for 2x(x+4)+x^2-3(4x-7)x=6x^2+12 equation: 


Simplifying
2x(x + 4) + x2 + -3(4x + -7) * x = 6x2 + 12

Reorder the terms:
2x(4 + x) + x2 + -3(4x + -7) * x = 6x2 + 12
(4 * 2x + x * 2x) + x2 + -3(4x + -7) * x = 6x2 + 12
(8x + 2x2) + x2 + -3(4x + -7) * x = 6x2 + 12

Reorder the terms:
8x + 2x2 + x2 + -3(-7 + 4x) * x = 6x2 + 12

Reorder the terms for easier multiplication:
8x + 2x2 + x2 + -3x(-7 + 4x) = 6x2 + 12
8x + 2x2 + x2 + (-7 * -3x + 4x * -3x) = 6x2 + 12
8x + 2x2 + x2 + (21x + -12x2) = 6x2 + 12

Reorder the terms:
8x + 21x + 2x2 + x2 + -12x2 = 6x2 + 12

Combine like terms: 8x + 21x = 29x
29x + 2x2 + x2 + -12x2 = 6x2 + 12

Combine like terms: 2x2 + x2 = 3x2
29x + 3x2 + -12x2 = 6x2 + 12

Combine like terms: 3x2 + -12x2 = -9x2
29x + -9x2 = 6x2 + 12

Reorder the terms:
29x + -9x2 = 12 + 6x2

Solving
29x + -9x2 = 12 + 6x2

Solving for variable 'x'.

Reorder the terms:
-12 + 29x + -9x2 + -6x2 = 12 + 6x2 + -12 + -6x2

Combine like terms: -9x2 + -6x2 = -15x2
-12 + 29x + -15x2 = 12 + 6x2 + -12 + -6x2

Reorder the terms:
-12 + 29x + -15x2 = 12 + -12 + 6x2 + -6x2

Combine like terms: 12 + -12 = 0
-12 + 29x + -15x2 = 0 + 6x2 + -6x2
-12 + 29x + -15x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-12 + 29x + -15x2 = 0

Factor a trinomial.
(-4 + 3x)(3 + -5x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {1.333333333, 0.6}

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