(4x-3)(x+7)=(x-3)(1-5x)

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Solution for (4x-3)(x+7)=(x-3)(1-5x) equation: 


Simplifying
(4x + -3)(x + 7) = (x + -3)(1 + -5x)

Reorder the terms:
(-3 + 4x)(x + 7) = (x + -3)(1 + -5x)

Reorder the terms:
(-3 + 4x)(7 + x) = (x + -3)(1 + -5x)

Multiply (-3 + 4x) * (7 + x)
(-3(7 + x) + 4x * (7 + x)) = (x + -3)(1 + -5x)
((7 * -3 + x * -3) + 4x * (7 + x)) = (x + -3)(1 + -5x)
((-21 + -3x) + 4x * (7 + x)) = (x + -3)(1 + -5x)
(-21 + -3x + (7 * 4x + x * 4x)) = (x + -3)(1 + -5x)
(-21 + -3x + (28x + 4x2)) = (x + -3)(1 + -5x)

Combine like terms: -3x + 28x = 25x
(-21 + 25x + 4x2) = (x + -3)(1 + -5x)

Reorder the terms:
-21 + 25x + 4x2 = (-3 + x)(1 + -5x)

Multiply (-3 + x) * (1 + -5x)
-21 + 25x + 4x2 = (-3(1 + -5x) + x(1 + -5x))
-21 + 25x + 4x2 = ((1 * -3 + -5x * -3) + x(1 + -5x))
-21 + 25x + 4x2 = ((-3 + 15x) + x(1 + -5x))
-21 + 25x + 4x2 = (-3 + 15x + (1 * x + -5x * x))
-21 + 25x + 4x2 = (-3 + 15x + (1x + -5x2))

Combine like terms: 15x + 1x = 16x
-21 + 25x + 4x2 = (-3 + 16x + -5x2)

Solving
-21 + 25x + 4x2 = -3 + 16x + -5x2

Solving for variable 'x'.

Reorder the terms:
-21 + 3 + 25x + -16x + 4x2 + 5x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Combine like terms: -21 + 3 = -18
-18 + 25x + -16x + 4x2 + 5x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Combine like terms: 25x + -16x = 9x
-18 + 9x + 4x2 + 5x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Combine like terms: 4x2 + 5x2 = 9x2
-18 + 9x + 9x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Reorder the terms:
-18 + 9x + 9x2 = -3 + 3 + 16x + -16x + -5x2 + 5x2

Combine like terms: -3 + 3 = 0
-18 + 9x + 9x2 = 0 + 16x + -16x + -5x2 + 5x2
-18 + 9x + 9x2 = 16x + -16x + -5x2 + 5x2

Combine like terms: 16x + -16x = 0
-18 + 9x + 9x2 = 0 + -5x2 + 5x2
-18 + 9x + 9x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-18 + 9x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + x + x2) = 0

Factor a trinomial.
9((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 9.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 1}

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