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

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


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

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

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

Multiply (-2 + x) * (5 + x)
(-2(5 + x) + x(5 + x)) + 3x + -2 = -21
((5 * -2 + x * -2) + x(5 + x)) + 3x + -2 = -21
((-10 + -2x) + x(5 + x)) + 3x + -2 = -21
(-10 + -2x + (5 * x + x * x)) + 3x + -2 = -21
(-10 + -2x + (5x + x2)) + 3x + -2 = -21

Combine like terms: -2x + 5x = 3x
(-10 + 3x + x2) + 3x + -2 = -21

Reorder the terms:
-10 + -2 + 3x + 3x + x2 = -21

Combine like terms: -10 + -2 = -12
-12 + 3x + 3x + x2 = -21

Combine like terms: 3x + 3x = 6x
-12 + 6x + x2 = -21

Solving
-12 + 6x + x2 = -21

Solving for variable 'x'.

Reorder the terms:
-12 + 21 + 6x + x2 = -21 + 21

Combine like terms: -12 + 21 = 9
9 + 6x + x2 = -21 + 21

Combine like terms: -21 + 21 = 0
9 + 6x + x2 = 0

Factor a trinomial.
(3 + x)(3 + x) = 0

Subproblem 1

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

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 = {-3, -3}

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