16x(x+3)=142-(4x-11)*6

Solution for 16x(x+3)=142-(4x-11)*6 equation:

Simplifying
16x(x + 3) = 142 + -1(4x + -11) * 6

Reorder the terms:
16x(3 + x) = 142 + -1(4x + -11) * 6
(3 * 16x + x * 16x) = 142 + -1(4x + -11) * 6
(48x + 16x2) = 142 + -1(4x + -11) * 6

Reorder the terms:
48x + 16x2 = 142 + -1(-11 + 4x) * 6

Reorder the terms for easier multiplication:
48x + 16x2 = 142 + -1 * 6(-11 + 4x)

Multiply -1 * 6
48x + 16x2 = 142 + -6(-11 + 4x)
48x + 16x2 = 142 + (-11 * -6 + 4x * -6)
48x + 16x2 = 142 + (66 + -24x)

Combine like terms: 142 + 66 = 208
48x + 16x2 = 208 + -24x

Solving
48x + 16x2 = 208 + -24x

Solving for variable 'x'.

Reorder the terms:
-208 + 48x + 24x + 16x2 = 208 + -24x + -208 + 24x

Combine like terms: 48x + 24x = 72x
-208 + 72x + 16x2 = 208 + -24x + -208 + 24x

Reorder the terms:
-208 + 72x + 16x2 = 208 + -208 + -24x + 24x

Combine like terms: 208 + -208 = 0
-208 + 72x + 16x2 = 0 + -24x + 24x
-208 + 72x + 16x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-208 + 72x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-26 + 9x + 2x2) = 0

Factor a trinomial.
8((-13 + -2x)(2 + -1x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-6.5, 2}