40=(2x+3)(x+7)

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Solution for 40=(2x+3)(x+7) equation:


Simplifying
40 = (2x + 3)(x + 7)

Reorder the terms:
40 = (3 + 2x)(x + 7)

Reorder the terms:
40 = (3 + 2x)(7 + x)

Multiply (3 + 2x) * (7 + x)
40 = (3(7 + x) + 2x * (7 + x))
40 = ((7 * 3 + x * 3) + 2x * (7 + x))
40 = ((21 + 3x) + 2x * (7 + x))
40 = (21 + 3x + (7 * 2x + x * 2x))
40 = (21 + 3x + (14x + 2x2))

Combine like terms: 3x + 14x = 17x
40 = (21 + 17x + 2x2)

Solving
40 = 21 + 17x + 2x2

Solving for variable 'x'.

Combine like terms: 40 + -21 = 19
19 + -17x + -2x2 = 21 + 17x + 2x2 + -21 + -17x + -2x2

Reorder the terms:
19 + -17x + -2x2 = 21 + -21 + 17x + -17x + 2x2 + -2x2

Combine like terms: 21 + -21 = 0
19 + -17x + -2x2 = 0 + 17x + -17x + 2x2 + -2x2
19 + -17x + -2x2 = 17x + -17x + 2x2 + -2x2

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

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

Factor a trinomial.
(1 + -1x)(19 + 2x) = 0

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 '(19 + 2x)' equal to zero and attempt to solve: Simplifying 19 + 2x = 0 Solving 19 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 2x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 2x = 0 + -19 2x = 0 + -19 Combine like terms: 0 + -19 = -19 2x = -19 Divide each side by '2'. x = -9.5 Simplifying x = -9.5

Solution

x = {1, -9.5}

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