4(x-2)10x=-40

Solution for 4(x-2)10x=-40 equation:

Simplifying
4(x + -2) * 10x = -40

Reorder the terms:
4(-2 + x) * 10x = -40

Reorder the terms for easier multiplication:
4 * 10x(-2 + x) = -40

Multiply 4 * 10
40x(-2 + x) = -40
(-2 * 40x + x * 40x) = -40
(-80x + 40x2) = -40

Solving
-80x + 40x2 = -40

Solving for variable 'x'.

Reorder the terms:
40 + -80x + 40x2 = -40 + 40

Combine like terms: -40 + 40 = 0
40 + -80x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '40'.
40(1 + -2x + x2) = 0

Factor a trinomial.
40((1 + -1x)(1 + -1x)) = 0

Ignore the factor 40.
Subproblem 1
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
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 = {1, 1}