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

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


Simplifying
7x(4 + -3x) = 5 + (3x + -1)
(4 * 7x + -3x * 7x) = 5 + (3x + -1)
(28x + -21x2) = 5 + (3x + -1)

Reorder the terms:
28x + -21x2 = 5 + (-1 + 3x)

Remove parenthesis around (-1 + 3x)
28x + -21x2 = 5 + -1 + 3x

Combine like terms: 5 + -1 = 4
28x + -21x2 = 4 + 3x

Solving
28x + -21x2 = 4 + 3x

Solving for variable 'x'.

Reorder the terms:
-4 + 28x + -3x + -21x2 = 4 + 3x + -4 + -3x

Combine like terms: 28x + -3x = 25x
-4 + 25x + -21x2 = 4 + 3x + -4 + -3x

Reorder the terms:
-4 + 25x + -21x2 = 4 + -4 + 3x + -3x

Combine like terms: 4 + -4 = 0
-4 + 25x + -21x2 = 0 + 3x + -3x
-4 + 25x + -21x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-4 + 25x + -21x2 = 0

Factor a trinomial.
(-1 + x)(4 + -21x) = 0


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

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(4 + -21x)' equal to zero and attempt to solve:

Simplifying
4 + -21x = 0

Solving
4 + -21x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -21x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -21x = 0 + -4
-21x = 0 + -4

Combine like terms: 0 + -4 = -4
-21x = -4

Divide each side by '-21'.
x = 0.1904761905

Simplifying
x = 0.1904761905
Solution
x = {1, 0.1904761905}

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