4(x-5)+6=2x(x-6)

Solution for 4(x-5)+6=2x(x-6) equation:

Simplifying
4(x + -5) + 6 = 2x(x + -6)

Reorder the terms:
4(-5 + x) + 6 = 2x(x + -6)
(-5 * 4 + x * 4) + 6 = 2x(x + -6)
(-20 + 4x) + 6 = 2x(x + -6)

Reorder the terms:
-20 + 6 + 4x = 2x(x + -6)

Combine like terms: -20 + 6 = -14
-14 + 4x = 2x(x + -6)

Reorder the terms:
-14 + 4x = 2x(-6 + x)
-14 + 4x = (-6 * 2x + x * 2x)
-14 + 4x = (-12x + 2x2)

Solving
-14 + 4x = -12x + 2x2

Solving for variable 'x'.

Combine like terms: 4x + 12x = 16x
-14 + 16x + -2x2 = -12x + 2x2 + 12x + -2x2

Reorder the terms:
-14 + 16x + -2x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
-14 + 16x + -2x2 = 0 + 2x2 + -2x2
-14 + 16x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-14 + 16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 8x + -1x2) = 0

Factor a trinomial.
2((-7 + x)(1 + -1x)) = 0

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

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

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

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

Simplifying
x = 7
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 = {7, 1}