7+3x(1-x)=5-2(3-4x)

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Solution for 7+3x(1-x)=5-2(3-4x) equation: 


Simplifying
7 + 3x(1 + -1x) = 5 + -2(3 + -4x)
7 + (1 * 3x + -1x * 3x) = 5 + -2(3 + -4x)
7 + (3x + -3x2) = 5 + -2(3 + -4x)
7 + 3x + -3x2 = 5 + (3 * -2 + -4x * -2)
7 + 3x + -3x2 = 5 + (-6 + 8x)

Combine like terms: 5 + -6 = -1
7 + 3x + -3x2 = -1 + 8x

Solving
7 + 3x + -3x2 = -1 + 8x

Solving for variable 'x'.

Reorder the terms:
7 + 1 + 3x + -8x + -3x2 = -1 + 8x + 1 + -8x

Combine like terms: 7 + 1 = 8
8 + 3x + -8x + -3x2 = -1 + 8x + 1 + -8x

Combine like terms: 3x + -8x = -5x
8 + -5x + -3x2 = -1 + 8x + 1 + -8x

Reorder the terms:
8 + -5x + -3x2 = -1 + 1 + 8x + -8x

Combine like terms: -1 + 1 = 0
8 + -5x + -3x2 = 0 + 8x + -8x
8 + -5x + -3x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
8 + -5x + -3x2 = 0

Factor a trinomial.
(1 + -1x)(8 + 3x) = 0


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 '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667
Solution
x = {1, -2.666666667}

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