(x-2)(x+5)=7x-10

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Solution for (x-2)(x+5)=7x-10 equation: 


Simplifying
(x + -2)(x + 5) = 7x + -10

Reorder the terms:
(-2 + x)(x + 5) = 7x + -10

Reorder the terms:
(-2 + x)(5 + x) = 7x + -10

Multiply (-2 + x) * (5 + x)
(-2(5 + x) + x(5 + x)) = 7x + -10
((5 * -2 + x * -2) + x(5 + x)) = 7x + -10
((-10 + -2x) + x(5 + x)) = 7x + -10
(-10 + -2x + (5 * x + x * x)) = 7x + -10
(-10 + -2x + (5x + x2)) = 7x + -10

Combine like terms: -2x + 5x = 3x
(-10 + 3x + x2) = 7x + -10

Reorder the terms:
-10 + 3x + x2 = -10 + 7x

Add '10' to each side of the equation.
-10 + 3x + 10 + x2 = -10 + 10 + 7x

Reorder the terms:
-10 + 10 + 3x + x2 = -10 + 10 + 7x

Combine like terms: -10 + 10 = 0
0 + 3x + x2 = -10 + 10 + 7x
3x + x2 = -10 + 10 + 7x

Combine like terms: -10 + 10 = 0
3x + x2 = 0 + 7x
3x + x2 = 7x

Solving
3x + x2 = 7x

Solving for variable 'x'.

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

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

Combine like terms: 7x + -7x = 0
-4x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

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

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

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

Simplifying
x = 4
Solution
x = {0, 4}

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