-4x(x-7)+6(2x-7)=3x-9x

Solution for -4x(x-7)+6(2x-7)=3x-9x equation:

Simplifying
-4x(x + -7) + 6(2x + -7) = 3x + -9x

Reorder the terms:
-4x(-7 + x) + 6(2x + -7) = 3x + -9x
(-7 * -4x + x * -4x) + 6(2x + -7) = 3x + -9x
(28x + -4x2) + 6(2x + -7) = 3x + -9x

Reorder the terms:
28x + -4x2 + 6(-7 + 2x) = 3x + -9x
28x + -4x2 + (-7 * 6 + 2x * 6) = 3x + -9x
28x + -4x2 + (-42 + 12x) = 3x + -9x

Reorder the terms:
-42 + 28x + 12x + -4x2 = 3x + -9x

Combine like terms: 28x + 12x = 40x
-42 + 40x + -4x2 = 3x + -9x

Combine like terms: 3x + -9x = -6x
-42 + 40x + -4x2 = -6x

Solving
-42 + 40x + -4x2 = -6x

Solving for variable 'x'.

Reorder the terms:
-42 + 40x + 6x + -4x2 = -6x + 6x

Combine like terms: 40x + 6x = 46x
-42 + 46x + -4x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-42 + 46x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 23x + -2x2) = 0

Factor a trinomial.
2((-21 + 2x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + 2x)' equal to zero and attempt to solve:

Simplifying
-21 + 2x = 0

Solving
-21 + 2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + 2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2x = 0 + 21
2x = 0 + 21

Combine like terms: 0 + 21 = 21
2x = 21

Divide each side by '2'.
x = 10.5

Simplifying
x = 10.5
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 = {10.5, 1}