7(1-x)=(2x+3)(1-x)

Solution for 7(1-x)=(2x+3)(1-x) equation:

Simplifying
7(1 + -1x) = (2x + 3)(1 + -1x)
(1 * 7 + -1x * 7) = (2x + 3)(1 + -1x)
(7 + -7x) = (2x + 3)(1 + -1x)

Reorder the terms:
7 + -7x = (3 + 2x)(1 + -1x)

Multiply (3 + 2x) * (1 + -1x)
7 + -7x = (3(1 + -1x) + 2x * (1 + -1x))
7 + -7x = ((1 * 3 + -1x * 3) + 2x * (1 + -1x))
7 + -7x = ((3 + -3x) + 2x * (1 + -1x))
7 + -7x = (3 + -3x + (1 * 2x + -1x * 2x))
7 + -7x = (3 + -3x + (2x + -2x2))

Combine like terms: -3x + 2x = -1x
7 + -7x = (3 + -1x + -2x2)

Solving
7 + -7x = 3 + -1x + -2x2

Solving for variable 'x'.

Reorder the terms:
7 + -3 + -7x + x + 2x2 = 3 + -1x + -2x2 + -3 + x + 2x2

Combine like terms: 7 + -3 = 4
4 + -7x + x + 2x2 = 3 + -1x + -2x2 + -3 + x + 2x2

Combine like terms: -7x + x = -6x
4 + -6x + 2x2 = 3 + -1x + -2x2 + -3 + x + 2x2

Reorder the terms:
4 + -6x + 2x2 = 3 + -3 + -1x + x + -2x2 + 2x2

Combine like terms: 3 + -3 = 0
4 + -6x + 2x2 = 0 + -1x + x + -2x2 + 2x2
4 + -6x + 2x2 = -1x + x + -2x2 + 2x2

Combine like terms: -1x + x = 0
4 + -6x + 2x2 = 0 + -2x2 + 2x2
4 + -6x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
4 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3x + x2) = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
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 = {1, 2}