24x^2=3(43x-15)

Solution for 24x^2=3(43x-15) equation:

Simplifying
24x2 = 3(43x + -15)

Reorder the terms:
24x2 = 3(-15 + 43x)
24x2 = (-15 * 3 + 43x * 3)
24x2 = (-45 + 129x)

Solving
24x2 = -45 + 129x

Solving for variable 'x'.

Reorder the terms:
45 + -129x + 24x2 = -45 + 129x + 45 + -129x

Reorder the terms:
45 + -129x + 24x2 = -45 + 45 + 129x + -129x

Combine like terms: -45 + 45 = 0
45 + -129x + 24x2 = 0 + 129x + -129x
45 + -129x + 24x2 = 129x + -129x

Combine like terms: 129x + -129x = 0
45 + -129x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + -43x + 8x2) = 0

Factor a trinomial.
3((3 + -8x)(5 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -8x)' equal to zero and attempt to solve:

Simplifying
3 + -8x = 0

Solving
3 + -8x = 0

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

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

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

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

Divide each side by '-8'.
x = 0.375

Simplifying
x = 0.375
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0.375, 5}