4*(x-1)-(2-2x)*(2x+5)=0

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Solution for 4*(x-1)-(2-2x)*(2x+5)=0 equation: 


Simplifying
4(x + -1) + -1(2 + -2x)(2x + 5) = 0

Reorder the terms:
4(-1 + x) + -1(2 + -2x)(2x + 5) = 0
(-1 * 4 + x * 4) + -1(2 + -2x)(2x + 5) = 0
(-4 + 4x) + -1(2 + -2x)(2x + 5) = 0

Reorder the terms:
-4 + 4x + -1(2 + -2x)(5 + 2x) = 0

Multiply (2 + -2x) * (5 + 2x)
-4 + 4x + -1(2(5 + 2x) + -2x * (5 + 2x)) = 0
-4 + 4x + -1((5 * 2 + 2x * 2) + -2x * (5 + 2x)) = 0
-4 + 4x + -1((10 + 4x) + -2x * (5 + 2x)) = 0
-4 + 4x + -1(10 + 4x + (5 * -2x + 2x * -2x)) = 0
-4 + 4x + -1(10 + 4x + (-10x + -4x2)) = 0

Combine like terms: 4x + -10x = -6x
-4 + 4x + -1(10 + -6x + -4x2) = 0
-4 + 4x + (10 * -1 + -6x * -1 + -4x2 * -1) = 0
-4 + 4x + (-10 + 6x + 4x2) = 0

Reorder the terms:
-4 + -10 + 4x + 6x + 4x2 = 0

Combine like terms: -4 + -10 = -14
-14 + 4x + 6x + 4x2 = 0

Combine like terms: 4x + 6x = 10x
-14 + 10x + 4x2 = 0

Solving
-14 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 5x + 2x2) = 0

Factor a trinomial.
2((-7 + -2x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, 1}

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