(x+7)(7x-1)=43x+5x^2

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Solution for (x+7)(7x-1)=43x+5x^2 equation: 


Simplifying
(x + 7)(7x + -1) = 43x + 5x2

Reorder the terms:
(7 + x)(7x + -1) = 43x + 5x2

Reorder the terms:
(7 + x)(-1 + 7x) = 43x + 5x2

Multiply (7 + x) * (-1 + 7x)
(7(-1 + 7x) + x(-1 + 7x)) = 43x + 5x2
((-1 * 7 + 7x * 7) + x(-1 + 7x)) = 43x + 5x2
((-7 + 49x) + x(-1 + 7x)) = 43x + 5x2
(-7 + 49x + (-1 * x + 7x * x)) = 43x + 5x2
(-7 + 49x + (-1x + 7x2)) = 43x + 5x2

Combine like terms: 49x + -1x = 48x
(-7 + 48x + 7x2) = 43x + 5x2

Solving
-7 + 48x + 7x2 = 43x + 5x2

Solving for variable 'x'.

Reorder the terms:
-7 + 48x + -43x + 7x2 + -5x2 = 43x + 5x2 + -43x + -5x2

Combine like terms: 48x + -43x = 5x
-7 + 5x + 7x2 + -5x2 = 43x + 5x2 + -43x + -5x2

Combine like terms: 7x2 + -5x2 = 2x2
-7 + 5x + 2x2 = 43x + 5x2 + -43x + -5x2

Reorder the terms:
-7 + 5x + 2x2 = 43x + -43x + 5x2 + -5x2

Combine like terms: 43x + -43x = 0
-7 + 5x + 2x2 = 0 + 5x2 + -5x2
-7 + 5x + 2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-7 + 5x + 2x2 = 0

Factor a trinomial.
(-7 + -2x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
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
Solution
x = {-3.5, 1}

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