3(x^2-5x+7)-2x^2=x^2+6x+3

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Solution for 3(x^2-5x+7)-2x^2=x^2+6x+3 equation: 


Simplifying
3(x2 + -5x + 7) + -2x2 = x2 + 6x + 3

Reorder the terms:
3(7 + -5x + x2) + -2x2 = x2 + 6x + 3
(7 * 3 + -5x * 3 + x2 * 3) + -2x2 = x2 + 6x + 3
(21 + -15x + 3x2) + -2x2 = x2 + 6x + 3

Combine like terms: 3x2 + -2x2 = 1x2
21 + -15x + 1x2 = x2 + 6x + 3

Reorder the terms:
21 + -15x + 1x2 = 3 + 6x + x2

Solving
21 + -15x + 1x2 = 3 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
21 + -3 + -15x + -6x + 1x2 + -1x2 = 3 + 6x + x2 + -3 + -6x + -1x2

Combine like terms: 21 + -3 = 18
18 + -15x + -6x + 1x2 + -1x2 = 3 + 6x + x2 + -3 + -6x + -1x2

Combine like terms: -15x + -6x = -21x
18 + -21x + 1x2 + -1x2 = 3 + 6x + x2 + -3 + -6x + -1x2

Combine like terms: 1x2 + -1x2 = 0
18 + -21x + 0 = 3 + 6x + x2 + -3 + -6x + -1x2
18 + -21x = 3 + 6x + x2 + -3 + -6x + -1x2

Reorder the terms:
18 + -21x = 3 + -3 + 6x + -6x + x2 + -1x2

Combine like terms: 3 + -3 = 0
18 + -21x = 0 + 6x + -6x + x2 + -1x2
18 + -21x = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
18 + -21x = 0 + x2 + -1x2
18 + -21x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
18 + -21x = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -7x) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(6 + -7x)' equal to zero and attempt to solve:

Simplifying
6 + -7x = 0

Solving
6 + -7x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7x = 0 + -6
-7x = 0 + -6

Combine like terms: 0 + -6 = -6
-7x = -6

Divide each side by '-7'.
x = 0.8571428571

Simplifying
x = 0.8571428571
Solution
x = {0.8571428571}

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