(x+5)(x+2)=130

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Solution for (x+5)(x+2)=130 equation:


Simplifying
(x + 5)(x + 2) = 130

Reorder the terms:
(5 + x)(x + 2) = 130

Reorder the terms:
(5 + x)(2 + x) = 130

Multiply (5 + x) * (2 + x)
(5(2 + x) + x(2 + x)) = 130
((2 * 5 + x * 5) + x(2 + x)) = 130
((10 + 5x) + x(2 + x)) = 130
(10 + 5x + (2 * x + x * x)) = 130
(10 + 5x + (2x + x2)) = 130

Combine like terms: 5x + 2x = 7x
(10 + 7x + x2) = 130

Solving
10 + 7x + x2 = 130

Solving for variable 'x'.

Reorder the terms:
10 + -130 + 7x + x2 = 130 + -130

Combine like terms: 10 + -130 = -120
-120 + 7x + x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-120 + 7x + x2 = 0

Factor a trinomial.
(-15 + -1x)(8 + -1x) = 0

Subproblem 1

Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-15, 8}

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