(x-3)(x+14)=10x

Solution for (x-3)(x+14)=10x equation:

Simplifying
(x + -3)(x + 14) = 10x

Reorder the terms:
(-3 + x)(x + 14) = 10x

Reorder the terms:
(-3 + x)(14 + x) = 10x

Multiply (-3 + x) * (14 + x)
(-3(14 + x) + x(14 + x)) = 10x
((14 * -3 + x * -3) + x(14 + x)) = 10x
((-42 + -3x) + x(14 + x)) = 10x
(-42 + -3x + (14 * x + x * x)) = 10x
(-42 + -3x + (14x + x2)) = 10x

Combine like terms: -3x + 14x = 11x
(-42 + 11x + x2) = 10x

Solving
-42 + 11x + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
-42 + 11x + -10x + x2 = 10x + -10x

Combine like terms: 11x + -10x = 1x
-42 + 1x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-42 + 1x + x2 = 0

Factor a trinomial.
(-7 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
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
Solution
x = {-7, 6}