(x+9)(4x-5)=(x+4)(1-3x)

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Solution for (x+9)(4x-5)=(x+4)(1-3x) equation: 


Simplifying
(x + 9)(4x + -5) = (x + 4)(1 + -3x)

Reorder the terms:
(9 + x)(4x + -5) = (x + 4)(1 + -3x)

Reorder the terms:
(9 + x)(-5 + 4x) = (x + 4)(1 + -3x)

Multiply (9 + x) * (-5 + 4x)
(9(-5 + 4x) + x(-5 + 4x)) = (x + 4)(1 + -3x)
((-5 * 9 + 4x * 9) + x(-5 + 4x)) = (x + 4)(1 + -3x)
((-45 + 36x) + x(-5 + 4x)) = (x + 4)(1 + -3x)
(-45 + 36x + (-5 * x + 4x * x)) = (x + 4)(1 + -3x)
(-45 + 36x + (-5x + 4x2)) = (x + 4)(1 + -3x)

Combine like terms: 36x + -5x = 31x
(-45 + 31x + 4x2) = (x + 4)(1 + -3x)

Reorder the terms:
-45 + 31x + 4x2 = (4 + x)(1 + -3x)

Multiply (4 + x) * (1 + -3x)
-45 + 31x + 4x2 = (4(1 + -3x) + x(1 + -3x))
-45 + 31x + 4x2 = ((1 * 4 + -3x * 4) + x(1 + -3x))
-45 + 31x + 4x2 = ((4 + -12x) + x(1 + -3x))
-45 + 31x + 4x2 = (4 + -12x + (1 * x + -3x * x))
-45 + 31x + 4x2 = (4 + -12x + (1x + -3x2))

Combine like terms: -12x + 1x = -11x
-45 + 31x + 4x2 = (4 + -11x + -3x2)

Solving
-45 + 31x + 4x2 = 4 + -11x + -3x2

Solving for variable 'x'.

Reorder the terms:
-45 + -4 + 31x + 11x + 4x2 + 3x2 = 4 + -11x + -3x2 + -4 + 11x + 3x2

Combine like terms: -45 + -4 = -49
-49 + 31x + 11x + 4x2 + 3x2 = 4 + -11x + -3x2 + -4 + 11x + 3x2

Combine like terms: 31x + 11x = 42x
-49 + 42x + 4x2 + 3x2 = 4 + -11x + -3x2 + -4 + 11x + 3x2

Combine like terms: 4x2 + 3x2 = 7x2
-49 + 42x + 7x2 = 4 + -11x + -3x2 + -4 + 11x + 3x2

Reorder the terms:
-49 + 42x + 7x2 = 4 + -4 + -11x + 11x + -3x2 + 3x2

Combine like terms: 4 + -4 = 0
-49 + 42x + 7x2 = 0 + -11x + 11x + -3x2 + 3x2
-49 + 42x + 7x2 = -11x + 11x + -3x2 + 3x2

Combine like terms: -11x + 11x = 0
-49 + 42x + 7x2 = 0 + -3x2 + 3x2
-49 + 42x + 7x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-49 + 42x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-7 + 6x + x2) = 0

Factor a trinomial.
7((-7 + -1x)(1 + -1x)) = 0

Ignore the factor 7.

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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
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
Solution
x = {-7, 1}

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