3(x+5)=2[x(7-x)]

Solution for 3(x+5)=2[x(7-x)] equation:

Simplifying
3(x + 5) = 2[x(7 + -1x)]

Reorder the terms:
3(5 + x) = 2[x(7 + -1x)]
(5 * 3 + x * 3) = 2[x(7 + -1x)]
(15 + 3x) = 2[x(7 + -1x)]
15 + 3x = 2[(7 * x + -1x * x)]
15 + 3x = 2[(7x + -1x2)]
15 + 3x = [7x * 2 + -1x2 * 2]
15 + 3x = [14x + -2x2]

Solving
15 + 3x = 14x + -2x2

Solving for variable 'x'.

Combine like terms: 3x + -14x = -11x
15 + -11x + 2x2 = 14x + -2x2 + -14x + 2x2

Reorder the terms:
15 + -11x + 2x2 = 14x + -14x + -2x2 + 2x2

Combine like terms: 14x + -14x = 0
15 + -11x + 2x2 = 0 + -2x2 + 2x2
15 + -11x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
15 + -11x + 2x2 = 0

Factor a trinomial.
(5 + -2x)(3 + -1x) = 0

Subproblem 1
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
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 = {2.5, 3}