5x-7x(x+3)=-2x-21

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Solution for 5x-7x(x+3)=-2x-21 equation: 


Simplifying
5x + -7x(x + 3) = -2x + -21

Reorder the terms:
5x + -7x(3 + x) = -2x + -21
5x + (3 * -7x + x * -7x) = -2x + -21
5x + (-21x + -7x2) = -2x + -21

Combine like terms: 5x + -21x = -16x
-16x + -7x2 = -2x + -21

Reorder the terms:
-16x + -7x2 = -21 + -2x

Solving
-16x + -7x2 = -21 + -2x

Solving for variable 'x'.

Reorder the terms:
21 + -16x + 2x + -7x2 = -21 + -2x + 21 + 2x

Combine like terms: -16x + 2x = -14x
21 + -14x + -7x2 = -21 + -2x + 21 + 2x

Reorder the terms:
21 + -14x + -7x2 = -21 + 21 + -2x + 2x

Combine like terms: -21 + 21 = 0
21 + -14x + -7x2 = 0 + -2x + 2x
21 + -14x + -7x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
21 + -14x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + -2x + -1x2) = 0

Factor a trinomial.
7((1 + -1x)(3 + x)) = 0

Ignore the factor 7.

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {1, -3}

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