(4x+7)(x-1)=2(x-2)

Solution for (4x+7)(x-1)=2(x-2) equation:

Simplifying
(4x + 7)(x + -1) = 2(x + -2)

Reorder the terms:
(7 + 4x)(x + -1) = 2(x + -2)

Reorder the terms:
(7 + 4x)(-1 + x) = 2(x + -2)

Multiply (7 + 4x) * (-1 + x)
(7(-1 + x) + 4x * (-1 + x)) = 2(x + -2)
((-1 * 7 + x * 7) + 4x * (-1 + x)) = 2(x + -2)
((-7 + 7x) + 4x * (-1 + x)) = 2(x + -2)
(-7 + 7x + (-1 * 4x + x * 4x)) = 2(x + -2)
(-7 + 7x + (-4x + 4x2)) = 2(x + -2)

Combine like terms: 7x + -4x = 3x
(-7 + 3x + 4x2) = 2(x + -2)

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

Solving
-7 + 3x + 4x2 = -4 + 2x

Solving for variable 'x'.

Reorder the terms:
-7 + 4 + 3x + -2x + 4x2 = -4 + 2x + 4 + -2x

Combine like terms: -7 + 4 = -3
-3 + 3x + -2x + 4x2 = -4 + 2x + 4 + -2x

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

Reorder the terms:
-3 + 1x + 4x2 = -4 + 4 + 2x + -2x

Combine like terms: -4 + 4 = 0
-3 + 1x + 4x2 = 0 + 2x + -2x
-3 + 1x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + 1x + 4x2 = 0

Factor a trinomial.
(-1 + -1x)(3 + -4x) = 0

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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1, 0.75}