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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