4x(x-7)-5x(x-6)=-3

Solution for 4x(x-7)-5x(x-6)=-3 equation:

Simplifying
4x(x + -7) + -5x(x + -6) = -3

Reorder the terms:
4x(-7 + x) + -5x(x + -6) = -3
(-7 * 4x + x * 4x) + -5x(x + -6) = -3
(-28x + 4x2) + -5x(x + -6) = -3

Reorder the terms:
-28x + 4x2 + -5x(-6 + x) = -3
-28x + 4x2 + (-6 * -5x + x * -5x) = -3
-28x + 4x2 + (30x + -5x2) = -3

Reorder the terms:
-28x + 30x + 4x2 + -5x2 = -3

Combine like terms: -28x + 30x = 2x
2x + 4x2 + -5x2 = -3

Combine like terms: 4x2 + -5x2 = -1x2
2x + -1x2 = -3

Solving
2x + -1x2 = -3

Solving for variable 'x'.

Reorder the terms:
3 + 2x + -1x2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 2x + -1x2 = 0

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

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {3, -1}