4x^2=28x-24

Solution for 4x^2=28x-24 equation:

Simplifying
4x2 = 28x + -24

Reorder the terms:
4x2 = -24 + 28x

Solving
4x2 = -24 + 28x

Solving for variable 'x'.

Reorder the terms:
24 + -28x + 4x2 = -24 + 28x + 24 + -28x

Reorder the terms:
24 + -28x + 4x2 = -24 + 24 + 28x + -28x

Combine like terms: -24 + 24 = 0
24 + -28x + 4x2 = 0 + 28x + -28x
24 + -28x + 4x2 = 28x + -28x

Combine like terms: 28x + -28x = 0
24 + -28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -7x + x2) = 0

Factor a trinomial.
4((1 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1, 6}