4x(x-7)=-48

Solution for 4x(x-7)=-48 equation:

Simplifying
4x(x + -7) = -48

Reorder the terms:
4x(-7 + x) = -48
(-7 * 4x + x * 4x) = -48
(-28x + 4x2) = -48

Solving
-28x + 4x2 = -48

Solving for variable 'x'.

Reorder the terms:
48 + -28x + 4x2 = -48 + 48

Combine like terms: -48 + 48 = 0
48 + -28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + -7x + x2) = 0

Factor a trinomial.
4((3 + -1x)(4 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {3, 4}