(4x+9)(x-7)-(8x+18)=0

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Solution for (4x+9)(x-7)-(8x+18)=0 equation: 


Simplifying
(4x + 9)(x + -7) + -1(8x + 18) = 0

Reorder the terms:
(9 + 4x)(x + -7) + -1(8x + 18) = 0

Reorder the terms:
(9 + 4x)(-7 + x) + -1(8x + 18) = 0

Multiply (9 + 4x) * (-7 + x)
(9(-7 + x) + 4x * (-7 + x)) + -1(8x + 18) = 0
((-7 * 9 + x * 9) + 4x * (-7 + x)) + -1(8x + 18) = 0
((-63 + 9x) + 4x * (-7 + x)) + -1(8x + 18) = 0
(-63 + 9x + (-7 * 4x + x * 4x)) + -1(8x + 18) = 0
(-63 + 9x + (-28x + 4x2)) + -1(8x + 18) = 0

Combine like terms: 9x + -28x = -19x
(-63 + -19x + 4x2) + -1(8x + 18) = 0

Reorder the terms:
-63 + -19x + 4x2 + -1(18 + 8x) = 0
-63 + -19x + 4x2 + (18 * -1 + 8x * -1) = 0
-63 + -19x + 4x2 + (-18 + -8x) = 0

Reorder the terms:
-63 + -18 + -19x + -8x + 4x2 = 0

Combine like terms: -63 + -18 = -81
-81 + -19x + -8x + 4x2 = 0

Combine like terms: -19x + -8x = -27x
-81 + -27x + 4x2 = 0

Solving
-81 + -27x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -4x)(9 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-2.25, 9}

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