21x^2-15x=12x-6

Solution for 21x^2-15x=12x-6 equation:

Simplifying
21x2 + -15x = 12x + -6

Reorder the terms:
-15x + 21x2 = 12x + -6

Reorder the terms:
-15x + 21x2 = -6 + 12x

Solving
-15x + 21x2 = -6 + 12x

Solving for variable 'x'.

Reorder the terms:
6 + -15x + -12x + 21x2 = -6 + 12x + 6 + -12x

Combine like terms: -15x + -12x = -27x
6 + -27x + 21x2 = -6 + 12x + 6 + -12x

Reorder the terms:
6 + -27x + 21x2 = -6 + 6 + 12x + -12x

Combine like terms: -6 + 6 = 0
6 + -27x + 21x2 = 0 + 12x + -12x
6 + -27x + 21x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
6 + -27x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -9x + 7x2) = 0

Factor a trinomial.
3((2 + -7x)(1 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
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 = {0.2857142857, 1}