(2x+7)(2x+5)=63

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Solution for (2x+7)(2x+5)=63 equation: 


Simplifying
(2x + 7)(2x + 5) = 63

Reorder the terms:
(7 + 2x)(2x + 5) = 63

Reorder the terms:
(7 + 2x)(5 + 2x) = 63

Multiply (7 + 2x) * (5 + 2x)
(7(5 + 2x) + 2x * (5 + 2x)) = 63
((5 * 7 + 2x * 7) + 2x * (5 + 2x)) = 63
((35 + 14x) + 2x * (5 + 2x)) = 63
(35 + 14x + (5 * 2x + 2x * 2x)) = 63
(35 + 14x + (10x + 4x2)) = 63

Combine like terms: 14x + 10x = 24x
(35 + 24x + 4x2) = 63

Solving
35 + 24x + 4x2 = 63

Solving for variable 'x'.

Reorder the terms:
35 + -63 + 24x + 4x2 = 63 + -63

Combine like terms: 35 + -63 = -28
-28 + 24x + 4x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-28 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + 6x + x2) = 0

Factor a trinomial.
4((-7 + -1x)(1 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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 = {-7, 1}

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