18=(2x+5)(x+7)

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Solution for 18=(2x+5)(x+7) equation:


Simplifying
18 = (2x + 5)(x + 7)

Reorder the terms:
18 = (5 + 2x)(x + 7)

Reorder the terms:
18 = (5 + 2x)(7 + x)

Multiply (5 + 2x) * (7 + x)
18 = (5(7 + x) + 2x * (7 + x))
18 = ((7 * 5 + x * 5) + 2x * (7 + x))
18 = ((35 + 5x) + 2x * (7 + x))
18 = (35 + 5x + (7 * 2x + x * 2x))
18 = (35 + 5x + (14x + 2x2))

Combine like terms: 5x + 14x = 19x
18 = (35 + 19x + 2x2)

Solving
18 = 35 + 19x + 2x2

Solving for variable 'x'.

Combine like terms: 18 + -35 = -17
-17 + -19x + -2x2 = 35 + 19x + 2x2 + -35 + -19x + -2x2

Reorder the terms:
-17 + -19x + -2x2 = 35 + -35 + 19x + -19x + 2x2 + -2x2

Combine like terms: 35 + -35 = 0
-17 + -19x + -2x2 = 0 + 19x + -19x + 2x2 + -2x2
-17 + -19x + -2x2 = 19x + -19x + 2x2 + -2x2

Combine like terms: 19x + -19x = 0
-17 + -19x + -2x2 = 0 + 2x2 + -2x2
-17 + -19x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-17 + -19x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(17 + 19x + 2x2) = 0

Factor a trinomial.
-1((17 + 2x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(17 + 2x)' equal to zero and attempt to solve: Simplifying 17 + 2x = 0 Solving 17 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 2x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 2x = 0 + -17 2x = 0 + -17 Combine like terms: 0 + -17 = -17 2x = -17 Divide each side by '2'. x = -8.5 Simplifying x = -8.5

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-8.5, -1}

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