4x(2x-7)=16

Solution for 4x(2x-7)=16 equation:

Simplifying
4x(2x + -7) = 16

Reorder the terms:
4x(-7 + 2x) = 16
(-7 * 4x + 2x * 4x) = 16
(-28x + 8x2) = 16

Solving
-28x + 8x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + -28x + 8x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -28x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -7x + 2x2) = 0

Factor a trinomial.
4((-1 + -2x)(4 + -1x)) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
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 = {-0.5, 4}