20(6)=4x(2x-7)

Solution for 20(6)=4x(2x-7) equation:

Simplifying
20(6) = 4x(2x + -7)

Multiply 20 * 6
120 = 4x(2x + -7)

Reorder the terms:
120 = 4x(-7 + 2x)
120 = (-7 * 4x + 2x * 4x)
120 = (-28x + 8x2)

Solving
120 = -28x + 8x2

Solving for variable 'x'.

Reorder the terms:
120 + 28x + -8x2 = -28x + 28x + 8x2 + -8x2

Combine like terms: -28x + 28x = 0
120 + 28x + -8x2 = 0 + 8x2 + -8x2
120 + 28x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
120 + 28x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + 7x + -2x2) = 0

Factor a trinomial.
4((6 + -1x)(5 + 2x)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {6, -2.5}