(3x-4)(x-9)=(x+15)(1-4x)

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Solution for (3x-4)(x-9)=(x+15)(1-4x) equation: 


Simplifying
(3x + -4)(x + -9) = (x + 15)(1 + -4x)

Reorder the terms:
(-4 + 3x)(x + -9) = (x + 15)(1 + -4x)

Reorder the terms:
(-4 + 3x)(-9 + x) = (x + 15)(1 + -4x)

Multiply (-4 + 3x) * (-9 + x)
(-4(-9 + x) + 3x * (-9 + x)) = (x + 15)(1 + -4x)
((-9 * -4 + x * -4) + 3x * (-9 + x)) = (x + 15)(1 + -4x)
((36 + -4x) + 3x * (-9 + x)) = (x + 15)(1 + -4x)
(36 + -4x + (-9 * 3x + x * 3x)) = (x + 15)(1 + -4x)
(36 + -4x + (-27x + 3x2)) = (x + 15)(1 + -4x)

Combine like terms: -4x + -27x = -31x
(36 + -31x + 3x2) = (x + 15)(1 + -4x)

Reorder the terms:
36 + -31x + 3x2 = (15 + x)(1 + -4x)

Multiply (15 + x) * (1 + -4x)
36 + -31x + 3x2 = (15(1 + -4x) + x(1 + -4x))
36 + -31x + 3x2 = ((1 * 15 + -4x * 15) + x(1 + -4x))
36 + -31x + 3x2 = ((15 + -60x) + x(1 + -4x))
36 + -31x + 3x2 = (15 + -60x + (1 * x + -4x * x))
36 + -31x + 3x2 = (15 + -60x + (1x + -4x2))

Combine like terms: -60x + 1x = -59x
36 + -31x + 3x2 = (15 + -59x + -4x2)

Solving
36 + -31x + 3x2 = 15 + -59x + -4x2

Solving for variable 'x'.

Reorder the terms:
36 + -15 + -31x + 59x + 3x2 + 4x2 = 15 + -59x + -4x2 + -15 + 59x + 4x2

Combine like terms: 36 + -15 = 21
21 + -31x + 59x + 3x2 + 4x2 = 15 + -59x + -4x2 + -15 + 59x + 4x2

Combine like terms: -31x + 59x = 28x
21 + 28x + 3x2 + 4x2 = 15 + -59x + -4x2 + -15 + 59x + 4x2

Combine like terms: 3x2 + 4x2 = 7x2
21 + 28x + 7x2 = 15 + -59x + -4x2 + -15 + 59x + 4x2

Reorder the terms:
21 + 28x + 7x2 = 15 + -15 + -59x + 59x + -4x2 + 4x2

Combine like terms: 15 + -15 = 0
21 + 28x + 7x2 = 0 + -59x + 59x + -4x2 + 4x2
21 + 28x + 7x2 = -59x + 59x + -4x2 + 4x2

Combine like terms: -59x + 59x = 0
21 + 28x + 7x2 = 0 + -4x2 + 4x2
21 + 28x + 7x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
21 + 28x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + 4x + x2) = 0

Factor a trinomial.
7((3 + x)(1 + x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3

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 = {-3, -1}

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