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

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


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

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

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

Multiply (-4 + 5x) * (7 + x)
(-4(7 + x) + 5x * (7 + x)) = (x + -3)(1 + -5x)
((7 * -4 + x * -4) + 5x * (7 + x)) = (x + -3)(1 + -5x)
((-28 + -4x) + 5x * (7 + x)) = (x + -3)(1 + -5x)
(-28 + -4x + (7 * 5x + x * 5x)) = (x + -3)(1 + -5x)
(-28 + -4x + (35x + 5x2)) = (x + -3)(1 + -5x)

Combine like terms: -4x + 35x = 31x
(-28 + 31x + 5x2) = (x + -3)(1 + -5x)

Reorder the terms:
-28 + 31x + 5x2 = (-3 + x)(1 + -5x)

Multiply (-3 + x) * (1 + -5x)
-28 + 31x + 5x2 = (-3(1 + -5x) + x(1 + -5x))
-28 + 31x + 5x2 = ((1 * -3 + -5x * -3) + x(1 + -5x))
-28 + 31x + 5x2 = ((-3 + 15x) + x(1 + -5x))
-28 + 31x + 5x2 = (-3 + 15x + (1 * x + -5x * x))
-28 + 31x + 5x2 = (-3 + 15x + (1x + -5x2))

Combine like terms: 15x + 1x = 16x
-28 + 31x + 5x2 = (-3 + 16x + -5x2)

Solving
-28 + 31x + 5x2 = -3 + 16x + -5x2

Solving for variable 'x'.

Reorder the terms:
-28 + 3 + 31x + -16x + 5x2 + 5x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Combine like terms: -28 + 3 = -25
-25 + 31x + -16x + 5x2 + 5x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Combine like terms: 31x + -16x = 15x
-25 + 15x + 5x2 + 5x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Combine like terms: 5x2 + 5x2 = 10x2
-25 + 15x + 10x2 = -3 + 16x + -5x2 + 3 + -16x + 5x2

Reorder the terms:
-25 + 15x + 10x2 = -3 + 3 + 16x + -16x + -5x2 + 5x2

Combine like terms: -3 + 3 = 0
-25 + 15x + 10x2 = 0 + 16x + -16x + -5x2 + 5x2
-25 + 15x + 10x2 = 16x + -16x + -5x2 + 5x2

Combine like terms: 16x + -16x = 0
-25 + 15x + 10x2 = 0 + -5x2 + 5x2
-25 + 15x + 10x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-25 + 15x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 3x + 2x2) = 0

Factor a trinomial.
5((-5 + -2x)(1 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 1}

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