(4x+9)(x+7)=8x+18

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Solution for (4x+9)(x+7)=8x+18 equation: 


Simplifying
(4x + 9)(x + 7) = 8x + 18

Reorder the terms:
(9 + 4x)(x + 7) = 8x + 18

Reorder the terms:
(9 + 4x)(7 + x) = 8x + 18

Multiply (9 + 4x) * (7 + x)
(9(7 + x) + 4x * (7 + x)) = 8x + 18
((7 * 9 + x * 9) + 4x * (7 + x)) = 8x + 18
((63 + 9x) + 4x * (7 + x)) = 8x + 18
(63 + 9x + (7 * 4x + x * 4x)) = 8x + 18
(63 + 9x + (28x + 4x2)) = 8x + 18

Combine like terms: 9x + 28x = 37x
(63 + 37x + 4x2) = 8x + 18

Reorder the terms:
63 + 37x + 4x2 = 18 + 8x

Solving
63 + 37x + 4x2 = 18 + 8x

Solving for variable 'x'.

Reorder the terms:
63 + -18 + 37x + -8x + 4x2 = 18 + 8x + -18 + -8x

Combine like terms: 63 + -18 = 45
45 + 37x + -8x + 4x2 = 18 + 8x + -18 + -8x

Combine like terms: 37x + -8x = 29x
45 + 29x + 4x2 = 18 + 8x + -18 + -8x

Reorder the terms:
45 + 29x + 4x2 = 18 + -18 + 8x + -8x

Combine like terms: 18 + -18 = 0
45 + 29x + 4x2 = 0 + 8x + -8x
45 + 29x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
45 + 29x + 4x2 = 0

Factor a trinomial.
(5 + x)(9 + 4x) = 0


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(9 + 4x)' equal to zero and attempt to solve:

Simplifying
9 + 4x = 0

Solving
9 + 4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4x = 0 + -9
4x = 0 + -9

Combine like terms: 0 + -9 = -9
4x = -9

Divide each side by '4'.
x = -2.25

Simplifying
x = -2.25
Solution
x = {-5, -2.25}

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