84=7x(2x+2)

Solution for 84=7x(2x+2) equation:

Simplifying
84 = 7x(2x + 2)

Reorder the terms:
84 = 7x(2 + 2x)
84 = (2 * 7x + 2x * 7x)
84 = (14x + 14x2)

Solving
84 = 14x + 14x2

Solving for variable 'x'.

Reorder the terms:
84 + -14x + -14x2 = 14x + -14x + 14x2 + -14x2

Combine like terms: 14x + -14x = 0
84 + -14x + -14x2 = 0 + 14x2 + -14x2
84 + -14x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
84 + -14x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '14'.
14(6 + -1x + -1x2) = 0

Factor a trinomial.
14((2 + -1x)(3 + x)) = 0

Ignore the factor 14.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {2, -3}