24x-21=3x^2

Solution for 24x-21=3x^2 equation:

Simplifying
24x + -21 = 3x2

Reorder the terms:
-21 + 24x = 3x2

Solving
-21 + 24x = 3x2

Solving for variable 'x'.

Combine like terms: 3x2 + -3x2 = 0
-21 + 24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 8x + -1x2) = 0

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

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

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

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

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

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

Simplifying
x = 7
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 = {7, 1}