21x^2-68x+32=0

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Solution for 21x^2-68x+32=0 equation: 


Simplifying
21x2 + -68x + 32 = 0

Reorder the terms:
32 + -68x + 21x2 = 0

Solving
32 + -68x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -7x)(8 + -3x) = 0


Subproblem 1
Set the factor '(4 + -7x)' equal to zero and attempt to solve:

Simplifying
4 + -7x = 0

Solving
4 + -7x = 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 + -7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7x = 0 + -4
-7x = 0 + -4

Combine like terms: 0 + -4 = -4
-7x = -4

Divide each side by '-7'.
x = 0.5714285714

Simplifying
x = 0.5714285714

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {0.5714285714, 2.666666667}

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