(2x+7)(x+8)=6x+35

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Solution for (2x+7)(x+8)=6x+35 equation: 


Simplifying
(2x + 7)(x + 8) = 6x + 35

Reorder the terms:
(7 + 2x)(x + 8) = 6x + 35

Reorder the terms:
(7 + 2x)(8 + x) = 6x + 35

Multiply (7 + 2x) * (8 + x)
(7(8 + x) + 2x * (8 + x)) = 6x + 35
((8 * 7 + x * 7) + 2x * (8 + x)) = 6x + 35
((56 + 7x) + 2x * (8 + x)) = 6x + 35
(56 + 7x + (8 * 2x + x * 2x)) = 6x + 35
(56 + 7x + (16x + 2x2)) = 6x + 35

Combine like terms: 7x + 16x = 23x
(56 + 23x + 2x2) = 6x + 35

Reorder the terms:
56 + 23x + 2x2 = 35 + 6x

Solving
56 + 23x + 2x2 = 35 + 6x

Solving for variable 'x'.

Reorder the terms:
56 + -35 + 23x + -6x + 2x2 = 35 + 6x + -35 + -6x

Combine like terms: 56 + -35 = 21
21 + 23x + -6x + 2x2 = 35 + 6x + -35 + -6x

Combine like terms: 23x + -6x = 17x
21 + 17x + 2x2 = 35 + 6x + -35 + -6x

Reorder the terms:
21 + 17x + 2x2 = 35 + -35 + 6x + -6x

Combine like terms: 35 + -35 = 0
21 + 17x + 2x2 = 0 + 6x + -6x
21 + 17x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
21 + 17x + 2x2 = 0

Factor a trinomial.
(7 + x)(3 + 2x) = 0


Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-7, -1.5}

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