6x^2=x^2-7x+12

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Solution for 6x^2=x^2-7x+12 equation: 


Simplifying
6x2 = x2 + -7x + 12

Reorder the terms:
6x2 = 12 + -7x + x2

Solving
6x2 = 12 + -7x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + 7x + 6x2 + -1x2 = 12 + -7x + x2 + -12 + 7x + -1x2

Combine like terms: 6x2 + -1x2 = 5x2
-12 + 7x + 5x2 = 12 + -7x + x2 + -12 + 7x + -1x2

Reorder the terms:
-12 + 7x + 5x2 = 12 + -12 + -7x + 7x + x2 + -1x2

Combine like terms: 12 + -12 = 0
-12 + 7x + 5x2 = 0 + -7x + 7x + x2 + -1x2
-12 + 7x + 5x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
-12 + 7x + 5x2 = 0 + x2 + -1x2
-12 + 7x + 5x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 7x + 5x2 = 0

Factor a trinomial.
(-12 + -5x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-12 + -5x)' equal to zero and attempt to solve:

Simplifying
-12 + -5x = 0

Solving
-12 + -5x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -5x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -5x = 0 + 12
-5x = 0 + 12

Combine like terms: 0 + 12 = 12
-5x = 12

Divide each side by '-5'.
x = -2.4

Simplifying
x = -2.4

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-2.4, 1}

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