(x+5)(4-7x)=(2x-9)(9x+5)

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Solution for (x+5)(4-7x)=(2x-9)(9x+5) equation: 


Simplifying
(x + 5)(4 + -7x) = (2x + -9)(9x + 5)

Reorder the terms:
(5 + x)(4 + -7x) = (2x + -9)(9x + 5)

Multiply (5 + x) * (4 + -7x)
(5(4 + -7x) + x(4 + -7x)) = (2x + -9)(9x + 5)
((4 * 5 + -7x * 5) + x(4 + -7x)) = (2x + -9)(9x + 5)
((20 + -35x) + x(4 + -7x)) = (2x + -9)(9x + 5)
(20 + -35x + (4 * x + -7x * x)) = (2x + -9)(9x + 5)
(20 + -35x + (4x + -7x2)) = (2x + -9)(9x + 5)

Combine like terms: -35x + 4x = -31x
(20 + -31x + -7x2) = (2x + -9)(9x + 5)

Reorder the terms:
20 + -31x + -7x2 = (-9 + 2x)(9x + 5)

Reorder the terms:
20 + -31x + -7x2 = (-9 + 2x)(5 + 9x)

Multiply (-9 + 2x) * (5 + 9x)
20 + -31x + -7x2 = (-9(5 + 9x) + 2x * (5 + 9x))
20 + -31x + -7x2 = ((5 * -9 + 9x * -9) + 2x * (5 + 9x))
20 + -31x + -7x2 = ((-45 + -81x) + 2x * (5 + 9x))
20 + -31x + -7x2 = (-45 + -81x + (5 * 2x + 9x * 2x))
20 + -31x + -7x2 = (-45 + -81x + (10x + 18x2))

Combine like terms: -81x + 10x = -71x
20 + -31x + -7x2 = (-45 + -71x + 18x2)

Solving
20 + -31x + -7x2 = -45 + -71x + 18x2

Solving for variable 'x'.

Reorder the terms:
20 + 45 + -31x + 71x + -7x2 + -18x2 = -45 + -71x + 18x2 + 45 + 71x + -18x2

Combine like terms: 20 + 45 = 65
65 + -31x + 71x + -7x2 + -18x2 = -45 + -71x + 18x2 + 45 + 71x + -18x2

Combine like terms: -31x + 71x = 40x
65 + 40x + -7x2 + -18x2 = -45 + -71x + 18x2 + 45 + 71x + -18x2

Combine like terms: -7x2 + -18x2 = -25x2
65 + 40x + -25x2 = -45 + -71x + 18x2 + 45 + 71x + -18x2

Reorder the terms:
65 + 40x + -25x2 = -45 + 45 + -71x + 71x + 18x2 + -18x2

Combine like terms: -45 + 45 = 0
65 + 40x + -25x2 = 0 + -71x + 71x + 18x2 + -18x2
65 + 40x + -25x2 = -71x + 71x + 18x2 + -18x2

Combine like terms: -71x + 71x = 0
65 + 40x + -25x2 = 0 + 18x2 + -18x2
65 + 40x + -25x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
65 + 40x + -25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(13 + 8x + -5x2) = 0

Factor a trinomial.
5((13 + -5x)(1 + x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(13 + -5x)' equal to zero and attempt to solve:

Simplifying
13 + -5x = 0

Solving
13 + -5x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -5x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -5x = 0 + -13
-5x = 0 + -13

Combine like terms: 0 + -13 = -13
-5x = -13

Divide each side by '-5'.
x = 2.6

Simplifying
x = 2.6

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {2.6, -1}

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