(4x-7)(x-6)=-56x+36

Solution for (4x-7)(x-6)=-56x+36 equation:

Simplifying
(4x + -7)(x + -6) = -56x + 36

Reorder the terms:
(-7 + 4x)(x + -6) = -56x + 36

Reorder the terms:
(-7 + 4x)(-6 + x) = -56x + 36

Multiply (-7 + 4x) * (-6 + x)
(-7(-6 + x) + 4x * (-6 + x)) = -56x + 36
((-6 * -7 + x * -7) + 4x * (-6 + x)) = -56x + 36
((42 + -7x) + 4x * (-6 + x)) = -56x + 36
(42 + -7x + (-6 * 4x + x * 4x)) = -56x + 36
(42 + -7x + (-24x + 4x2)) = -56x + 36

Combine like terms: -7x + -24x = -31x
(42 + -31x + 4x2) = -56x + 36

Reorder the terms:
42 + -31x + 4x2 = 36 + -56x

Solving
42 + -31x + 4x2 = 36 + -56x

Solving for variable 'x'.

Reorder the terms:
42 + -36 + -31x + 56x + 4x2 = 36 + -56x + -36 + 56x

Combine like terms: 42 + -36 = 6
6 + -31x + 56x + 4x2 = 36 + -56x + -36 + 56x

Combine like terms: -31x + 56x = 25x
6 + 25x + 4x2 = 36 + -56x + -36 + 56x

Reorder the terms:
6 + 25x + 4x2 = 36 + -36 + -56x + 56x

Combine like terms: 36 + -36 = 0
6 + 25x + 4x2 = 0 + -56x + 56x
6 + 25x + 4x2 = -56x + 56x

Combine like terms: -56x + 56x = 0
6 + 25x + 4x2 = 0

Factor a trinomial.
(6 + x)(1 + 4x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-6, -0.25}