(5x-3)(2-7x)=-35x+31x-6

Solution for (5x-3)(2-7x)=-35x+31x-6 equation:

Simplifying
(5x + -3)(2 + -7x) = -35x + 31x + -6

Reorder the terms:
(-3 + 5x)(2 + -7x) = -35x + 31x + -6

Multiply (-3 + 5x) * (2 + -7x)
(-3(2 + -7x) + 5x * (2 + -7x)) = -35x + 31x + -6
((2 * -3 + -7x * -3) + 5x * (2 + -7x)) = -35x + 31x + -6
((-6 + 21x) + 5x * (2 + -7x)) = -35x + 31x + -6
(-6 + 21x + (2 * 5x + -7x * 5x)) = -35x + 31x + -6
(-6 + 21x + (10x + -35x2)) = -35x + 31x + -6

Combine like terms: 21x + 10x = 31x
(-6 + 31x + -35x2) = -35x + 31x + -6

Reorder the terms:
-6 + 31x + -35x2 = -6 + -35x + 31x

Combine like terms: -35x + 31x = -4x
-6 + 31x + -35x2 = -6 + -4x

Add '6' to each side of the equation.
-6 + 31x + 6 + -35x2 = -6 + 6 + -4x

Reorder the terms:
-6 + 6 + 31x + -35x2 = -6 + 6 + -4x

Combine like terms: -6 + 6 = 0
0 + 31x + -35x2 = -6 + 6 + -4x
31x + -35x2 = -6 + 6 + -4x

Combine like terms: -6 + 6 = 0
31x + -35x2 = 0 + -4x
31x + -35x2 = -4x

Solving
31x + -35x2 = -4x

Solving for variable 'x'.

Reorder the terms:
31x + 4x + -35x2 = -4x + 4x

Combine like terms: 31x + 4x = 35x
35x + -35x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
35x + -35x2 = 0

Factor out the Greatest Common Factor (GCF), '35x'.
35x(1 + -1x) = 0

Ignore the factor 35.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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 = {0, 1}