(x+5)(7x-1)=32x+4x^2

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Solution for (x+5)(7x-1)=32x+4x^2 equation: 


Simplifying
(x + 5)(7x + -1) = 32x + 4x2

Reorder the terms:
(5 + x)(7x + -1) = 32x + 4x2

Reorder the terms:
(5 + x)(-1 + 7x) = 32x + 4x2

Multiply (5 + x) * (-1 + 7x)
(5(-1 + 7x) + x(-1 + 7x)) = 32x + 4x2
((-1 * 5 + 7x * 5) + x(-1 + 7x)) = 32x + 4x2
((-5 + 35x) + x(-1 + 7x)) = 32x + 4x2
(-5 + 35x + (-1 * x + 7x * x)) = 32x + 4x2
(-5 + 35x + (-1x + 7x2)) = 32x + 4x2

Combine like terms: 35x + -1x = 34x
(-5 + 34x + 7x2) = 32x + 4x2

Solving
-5 + 34x + 7x2 = 32x + 4x2

Solving for variable 'x'.

Reorder the terms:
-5 + 34x + -32x + 7x2 + -4x2 = 32x + 4x2 + -32x + -4x2

Combine like terms: 34x + -32x = 2x
-5 + 2x + 7x2 + -4x2 = 32x + 4x2 + -32x + -4x2

Combine like terms: 7x2 + -4x2 = 3x2
-5 + 2x + 3x2 = 32x + 4x2 + -32x + -4x2

Reorder the terms:
-5 + 2x + 3x2 = 32x + -32x + 4x2 + -4x2

Combine like terms: 32x + -32x = 0
-5 + 2x + 3x2 = 0 + 4x2 + -4x2
-5 + 2x + 3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5 + 2x + 3x2 = 0

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


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

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

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

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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 = {-1.666666667, 1}

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