(5x+3)(x-7)=5x(2)+3x-35x-21

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Solution for (5x+3)(x-7)=5x(2)+3x-35x-21 equation:


Simplifying
(5x + 3)(x + -7) = 5x(2) + 3x + -35x + -21

Reorder the terms:
(3 + 5x)(x + -7) = 5x(2) + 3x + -35x + -21

Reorder the terms:
(3 + 5x)(-7 + x) = 5x(2) + 3x + -35x + -21

Multiply (3 + 5x) * (-7 + x)
(3(-7 + x) + 5x * (-7 + x)) = 5x(2) + 3x + -35x + -21
((-7 * 3 + x * 3) + 5x * (-7 + x)) = 5x(2) + 3x + -35x + -21
((-21 + 3x) + 5x * (-7 + x)) = 5x(2) + 3x + -35x + -21
(-21 + 3x + (-7 * 5x + x * 5x)) = 5x(2) + 3x + -35x + -21
(-21 + 3x + (-35x + 5x2)) = 5x(2) + 3x + -35x + -21

Combine like terms: 3x + -35x = -32x
(-21 + -32x + 5x2) = 5x(2) + 3x + -35x + -21

Reorder the terms for easier multiplication:
-21 + -32x + 5x2 = 5 * 2x + 3x + -35x + -21

Multiply 5 * 2
-21 + -32x + 5x2 = 10x + 3x + -35x + -21

Reorder the terms:
-21 + -32x + 5x2 = -21 + 10x + 3x + -35x

Combine like terms: 10x + 3x = 13x
-21 + -32x + 5x2 = -21 + 13x + -35x

Combine like terms: 13x + -35x = -22x
-21 + -32x + 5x2 = -21 + -22x

Add '21' to each side of the equation.
-21 + -32x + 21 + 5x2 = -21 + 21 + -22x

Reorder the terms:
-21 + 21 + -32x + 5x2 = -21 + 21 + -22x

Combine like terms: -21 + 21 = 0
0 + -32x + 5x2 = -21 + 21 + -22x
-32x + 5x2 = -21 + 21 + -22x

Combine like terms: -21 + 21 = 0
-32x + 5x2 = 0 + -22x
-32x + 5x2 = -22x

Solving
-32x + 5x2 = -22x

Solving for variable 'x'.

Reorder the terms:
-32x + 22x + 5x2 = -22x + 22x

Combine like terms: -32x + 22x = -10x
-10x + 5x2 = -22x + 22x

Combine like terms: -22x + 22x = 0
-10x + 5x2 = 0

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

Ignore the factor 5.

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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2

Solution

x = {0, 2}

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