(7x-1)(5x+8)-(7x-1)(2x-3)=0

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Solution for (7x-1)(5x+8)-(7x-1)(2x-3)=0 equation:


Simplifying
(7x + -1)(5x + 8) + -1(7x + -1)(2x + -3) = 0

Reorder the terms:
(-1 + 7x)(5x + 8) + -1(7x + -1)(2x + -3) = 0

Reorder the terms:
(-1 + 7x)(8 + 5x) + -1(7x + -1)(2x + -3) = 0

Multiply (-1 + 7x) * (8 + 5x)
(-1(8 + 5x) + 7x * (8 + 5x)) + -1(7x + -1)(2x + -3) = 0
((8 * -1 + 5x * -1) + 7x * (8 + 5x)) + -1(7x + -1)(2x + -3) = 0
((-8 + -5x) + 7x * (8 + 5x)) + -1(7x + -1)(2x + -3) = 0
(-8 + -5x + (8 * 7x + 5x * 7x)) + -1(7x + -1)(2x + -3) = 0
(-8 + -5x + (56x + 35x2)) + -1(7x + -1)(2x + -3) = 0

Combine like terms: -5x + 56x = 51x
(-8 + 51x + 35x2) + -1(7x + -1)(2x + -3) = 0

Reorder the terms:
-8 + 51x + 35x2 + -1(-1 + 7x)(2x + -3) = 0

Reorder the terms:
-8 + 51x + 35x2 + -1(-1 + 7x)(-3 + 2x) = 0

Multiply (-1 + 7x) * (-3 + 2x)
-8 + 51x + 35x2 + -1(-1(-3 + 2x) + 7x * (-3 + 2x)) = 0
-8 + 51x + 35x2 + -1((-3 * -1 + 2x * -1) + 7x * (-3 + 2x)) = 0
-8 + 51x + 35x2 + -1((3 + -2x) + 7x * (-3 + 2x)) = 0
-8 + 51x + 35x2 + -1(3 + -2x + (-3 * 7x + 2x * 7x)) = 0
-8 + 51x + 35x2 + -1(3 + -2x + (-21x + 14x2)) = 0

Combine like terms: -2x + -21x = -23x
-8 + 51x + 35x2 + -1(3 + -23x + 14x2) = 0
-8 + 51x + 35x2 + (3 * -1 + -23x * -1 + 14x2 * -1) = 0
-8 + 51x + 35x2 + (-3 + 23x + -14x2) = 0

Reorder the terms:
-8 + -3 + 51x + 23x + 35x2 + -14x2 = 0

Combine like terms: -8 + -3 = -11
-11 + 51x + 23x + 35x2 + -14x2 = 0

Combine like terms: 51x + 23x = 74x
-11 + 74x + 35x2 + -14x2 = 0

Combine like terms: 35x2 + -14x2 = 21x2
-11 + 74x + 21x2 = 0

Solving
-11 + 74x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-11 + -3x)(1 + -7x) = 0


Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667

Subproblem 2
Set the factor '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

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

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

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

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Solution
x = {-3.666666667, 0.1428571429}

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