7x(3x+7)=11x-5

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Solution for 7x(3x+7)=11x-5 equation: 


Simplifying
7x(3x + 7) = 11x + -5

Reorder the terms:
7x(7 + 3x) = 11x + -5
(7 * 7x + 3x * 7x) = 11x + -5
(49x + 21x2) = 11x + -5

Reorder the terms:
49x + 21x2 = -5 + 11x

Solving
49x + 21x2 = -5 + 11x

Solving for variable 'x'.

Reorder the terms:
5 + 49x + -11x + 21x2 = -5 + 11x + 5 + -11x

Combine like terms: 49x + -11x = 38x
5 + 38x + 21x2 = -5 + 11x + 5 + -11x

Reorder the terms:
5 + 38x + 21x2 = -5 + 5 + 11x + -11x

Combine like terms: -5 + 5 = 0
5 + 38x + 21x2 = 0 + 11x + -11x
5 + 38x + 21x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
5 + 38x + 21x2 = 0

Factor a trinomial.
(5 + 3x)(1 + 7x) = 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 + 7x)' equal to zero and attempt to solve:

Simplifying
1 + 7x = 0

Solving
1 + 7x = 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 + 7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x = 0 + -1
7x = 0 + -1

Combine like terms: 0 + -1 = -1
7x = -1

Divide each side by '7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
Solution
x = {-1.666666667, -0.1428571429}

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