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

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

Simplifying
4x2 + -4x + 7x + -7 = 2(x + -1)

Reorder the terms:
-7 + -4x + 7x + 4x2 = 2(x + -1)

Combine like terms: -4x + 7x = 3x
-7 + 3x + 4x2 = 2(x + -1)

Reorder the terms:
-7 + 3x + 4x2 = 2(-1 + x)
-7 + 3x + 4x2 = (-1 * 2 + x * 2)
-7 + 3x + 4x2 = (-2 + 2x)

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

Solving for variable 'x'.

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

Combine like terms: -7 + 2 = -5
-5 + 3x + -2x + 4x2 = -2 + 2x + 2 + -2x

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

Reorder the terms:
-5 + 1x + 4x2 = -2 + 2 + 2x + -2x

Combine like terms: -2 + 2 = 0
-5 + 1x + 4x2 = 0 + 2x + -2x
-5 + 1x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-5 + 1x + 4x2 = 0

Factor a trinomial.
(-5 + -4x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25
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 = {-1.25, 1}