(10x+7)x=111

Solution for (10x+7)x=111 equation:

Simplifying
(10x + 7) * x = 111

Reorder the terms:
(7 + 10x) * x = 111

Reorder the terms for easier multiplication:
x(7 + 10x) = 111
(7 * x + 10x * x) = 111
(7x + 10x2) = 111

Solving
7x + 10x2 = 111

Solving for variable 'x'.

Reorder the terms:
-111 + 7x + 10x2 = 111 + -111

Combine like terms: 111 + -111 = 0
-111 + 7x + 10x2 = 0

Factor a trinomial.
(-37 + -10x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-37 + -10x)' equal to zero and attempt to solve:

Simplifying
-37 + -10x = 0

Solving
-37 + -10x = 0

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

Add '37' to each side of the equation.
-37 + 37 + -10x = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -10x = 0 + 37
-10x = 0 + 37

Combine like terms: 0 + 37 = 37
-10x = 37

Divide each side by '-10'.
x = -3.7

Simplifying
x = -3.7
Subproblem 2
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
Solution
x = {-3.7, 3}